From Brown Dwarfs to Super-Earths: An Observational Study of Weather and Atmospheric Composition

Transcription

1 UNIVERSITY OF EXETER From Brown Dwarfs to Super-Earths: An Observational Study of Weather and Atmospheric Composition Submitted by Paul Anthony Wilson to the University of Exeter as a thesis for the degree of Doctor of Philosophy in May 2014 This thesis is available for Library use on the understanding that it is copyright material and that no quotation from the thesis may be published without proper acknowledgement. I certify that all material in this thesis which is not my own work has been identified and that no material has previously been submitted and approved for the award of a degree by this or any other University. Signature:

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3 Abstract This PhD thesis presents work on the atmospheres of both brown dwarfs and exoplanets from an observers viewpoint. The composition and weather of these worlds are explored starting with M-type brown dwarfs and continuing through the L, T and Y spectral sequence, before entering the planetary regime of hot- Jupiters and super-earths. The similarities and differences between these objects such as their radii, surface gravities, pressures, temperatures and composition are discussed. This thesis presents new results from an extensive near-infrared monitoring survey of a uniform and unbiased sample of 69 L & T dwarfs spanning the L0 to T8 spectral range. Results show that amongst 14 identified variables, nine of them newly identified, variable brown dwarfs are not concentrated at the L - T transition, nor are they observed in a specific colour, or preferentially in binary systems. The thesis also presents narrow-band photometric measurements of the hot-jupiter HAT-P-1b and the super-earth GJ 1214b using the 10.4 m Gran Telescopio Canarias (GTC) and the OSIRIS instrument. Results for HAT-P-1b show a strong presence of potassium in the atmosphere caused by a large scale height, possibly due to higher than anticipated temperatures in the upper atmosphere or the dissociation of molecular hydrogen caused by the UV flux from the host star. Results for GJ 1214b, which constitute the first tunable filter measurements of a super-earth, find no evidence for the presence of methane showing a featureless transmission spectrum consistent with previous studies.

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5 Acknowledgements I still remember those cold winter nights sat outside my childhood house in Norway, staring at the night sky with the small telescope my father bought me in London. There was something magical about seeing Jupiter, Saturn and the countless other objects with my own eyes. Unlike the photographs in the books I had gotten from the local library or seen in the astronomy magazines, this was the real thing, the photons my eyes where collecting came directly from these celestial objects. It was my father, Anthony Berry Wilson, who discovered my interest for what it was and who helped me with my education. It is because of his encouragement and motivation in allowing me to pursue my love for astronomy that I undoubtedly owe the biggest thank you. I am also indebted to my friends and my family for their love and support. Along my long journey towards this PhD there have been many people which deserve a mention. Dr. Kim Venn for helping me with various applications. My office mates Alex Pettitt, Matt Willson and Hannah Wakeford with whom I have had many interesting conversations, and with whom I have managed to take so much of their productive time away from. My girlfriend at the time, Hollie Swain, for her understanding and support. Luke Smith for asking how my day has been and for bringing me coffee in the morning, accompanied by music. Francesca Booker for supporting me though the final stages of my PhD and for supporting me in her own unique way. Nathan Mayne, for being a great friend, mentor, make shift psychologist, advice machine and unofficial third supervisor. Abhijith Rajan and Prof. Jenny Patience for their fruitful collaboration and feedback on my work on brown dwarfs. Prof. Frédéric Pont for his supervision throughout the bulk of my PhD and for his support and humor. My internal and external assessors Dr. Sean Matt and Prof. David Pinfield for testing my knowledge during the viva. Last but not least, I would like to thank my supervisor, Dr. David K. Sing, for supervising me through the latter part of my PhD, for taking me on as a PhD student and for being an excellent collaborator and colleague. This research has benefited from the economic support of STFC and the free and open software provided by the Python communities and the developers of Ubuntu and all you other people contributing to various forums on the internet. You know who you are. iv

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7 vi The sun, with all those planets revolving around it and dependent on it, can still ripen a bunch of grapes as if it had nothing else in the universe to do. Galileo Galilei

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9 Contents Abstract ii Acknowledgements iv List of Figures List of Tables Declaration of Authorship xii xvi xviii Abbreviations Physical Constants xx xxii 1 Introduction Brown Dwarfs Definition Detection Techniques Brown Dwarf formation and evolution Characterising BD Atmospheres Spectral features of L,T and Y dwarfs Chemistry and Composition Variability at the L-T transition The Exoplanet-Brown Dwarf Connection The Shared Parameter Space Comparison of mass Comparison of radii Comparison of surface gravities and pressures Comparison of temperatures Comparison of composition Exoplanets A brief overview viii

10 Contents ix Detection techniques Direct imaging The Transit Method Exoplanet formation and evolution Formation via disk instability Core accretion model Planet-disk interaction and migration Inflated radii of extrasolar giant planets Compact radii of extrasolar giant planets Characterising Exoplanet Atmospheres Transmission Spectroscopy The Transmission Spectrum The effects of temperature on R The effects of changes in abundance on R The effects of mean molecular weight on R The Impacts of Stellar activity Thermal inversions Clouds and Hazes in Exoplanet Atmospheres Cloud models Observations & Data Reduction Observations in the optical The night sky in the optical Reducing optical imaging data Narrowband Spectrophotometry using tunable filters The Fabry-Pérot Interferometer Observations in the near-ir The near-ir sky Reducing near-ir imaging data High precision near-ir photometric monitoring of brown dwarfs Sources of noise Detector noise Shot noise The Signal-to-noise ratio Systematic noise Weather in the atmospheres of Brown Dwarfs The brown dwarf atmosphere monitoring (BAM) project. I. The largest near-ir monitoring survey of L and T dwarfs Abstract Introduction The BAM sample Observations Data Reduction and Photometry

11 Contents x Processing the images Generating the light curves Identifying variables Results of the BAM survey Comparison of variables with previous studies BAM Variables Variables in previous studies not confirmed with BAM Discussion The sensitivity of the BAM survey Frequency and amplitude of variability across spectral types Variability as a function of colour within a spectral type Binarity and variability Persistence of variability Summary Developments since publication Follow-up observations at the NOT and NTT The Atmospheres of Exoplanets Detection of potassium in HAT-P-1b from narrowband spectrophotometry Disclaimer Abstract Introduction Observations Instrumental setup Observing log Reductions Analysis Light curve fits Noise Estimate Results and Discussion The detection of potassium The effects of temperature The effects of potassium abundance and mean molecular weight The effects of resolution The effects of stellar variability The effects of systematics Conclusions A Search for Methane in the Atmosphere of GJ 1214b via GTC Narrow-Band Transmission Spectrophotometry Abstract

12 Contents xi Introduction Observations Å Transit, 17 August Å Transit, 2 June and 8835 Å Transit, 28 August and 8835 Å Transit, 10 June and Å Transit, 21 July Data Reduction Analysis Light curve fits The effects of Earth s Atmosphere The presence of sky lines Noise Estimate Results and Discussion Variability due to Stellar Activity The impact of the observed wavelength drifts Probing the methane feature Atmosphere models Conclusions Appendix: Short baselines and the radius ratio uncertainty Developments since publication Conclusions 163 A Markov Chain Monte Carlo 165 B p -value 167 B.1 Definition B.2 Calculating the p -value Bibliography 169

13 List of Figures 1.1 Effective temperature vs age for objects with masses ranging from 1 M Jup to 2.0 M The spectral standards VB 10 (M8), 2M0423 (T0) and 2M0415 (T8) shown with various different atomic and molecular bands Pressure-temperature profiles of model atmospheres Absolute MKO J magnitude as a function of J K colour and absolute MKO J magnitude as a function of spectral type Mass - Radius diagram showing the parameter space of stars, field BDs, young BDs and planets T eff & T eq Vs. log(g) Brightness temperature at K s wavelengths as a function of dayside equilibrium temperature Planetary mass (log(m Jup )) as a function of semi-major axis The impact parameter b Star-planet impact parameter geometry Star-planet impact parameter geometry Limb darkening geometry Light curves with different limb darkening coefficients Light curves with different inclination values Planetary radii as a function of incident flux Radius evolution tracks of a 4 M Jup object, representative of CoRoT- 20b The transit light curve V mag as a function of the atmospheric signal required to detect an atmospheric features 1 scale height in size Potassium line profiles showing the effects of temperature Potassium line profile showing the effects of abundance Potassium line profile shown for various m u The difference in transmission spectra with TiO/VO and without for a 1500 K isothermal, hydrostatic and uniform abundance model A wavelength and flux calibrated sky spectrum (black line) showing prominent emission lines together with broadband filter throughput curves The optical path of the Fabry-Pérot interferometer Fabry-Pérot fringe profile xii

14 List of Figures xiii 2.4 The near-ir sky transmission spectrum shown together with broadband filter throughput curves A wavelength and flux calibrated sky spectrum (black line) showing prominent emission lines together with broadband filter throughput curves A frame from the special flat sequence A raw SofI nodding image of a crowded field Colour-magnitude diagram of the M-L-T spectrum Histogram of the BAM sample across their respective spectral classes and the correspondin colour-colour diagram Target photometric uncertainty of the BAM survey p-value histogram of the full brown dwarf sample Final target light curves of the 14 variable objects Final target light curves of the candidate variables Final target light curves of a subset of constant objects in this survey with the master reference light curves Proportion of the survey sensitive to variability as a function of peak-to-trough amplitudes for different detection thresholds Variability frequency as a function of amplitude Percentage of simulated sinusoidal light curves detected as variable, as a function of period from 1 hour to 12 hours, for three different amplitudes Amplitude of the BAM variables and the target photometric uncertainty of the non-varying objects (coloured triangles) across the entire spectral range of the sample Histogram of the BAM sample across their respective spectral classes Histogram of the Radigan et al. (2014) sample across their respective spectral classes M observations with the NOT M observations with the NTT The Å HAT-P-1b light curve Light curves probing the potassium feature of HAT-P-1b Transmission spectrum of HAT-P-1b Best fit potassium line profile to the GTC observations of HAT-P-1b The HST/STIS G430L transmission spectrum of HAT-P-1b Changes in the planet-to-star radius ratio as function of bin width and resolution A surface plot of GJ 1214 showing an uneven PSF due to a misalignment of the M1 mirror The OSIRIS CCD1 (red) and CCD2 (blue) 500kHz exposure curves showing the linearity of the detector The posterior MCMC distribution showing the relationship between the radius ratio and the slope of the sky term Raw (non-detrended) transit light curves of GJ 1214b

15 List of Figures xiv 4.11 GTC OSIRIS narrow band light curves The GTC OSIRIS narrow band light curves at the off-methane target wavelengths The observed drift in OH sky emission observed during an observing sequence The GTC OSIRIS narrow band light curves Stellar variability of GJ 1214b The combined transmission spectrum of GJ 1214b The drift in wavelengths during each observation together with the changes in seeing and airmass The spectrum of GJ The weighted average of the on-methane and off-methane radius ratios The uncertainties on the radius ratio determinations

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17 List of Tables 3.1 L dwarf Sample T dwarf Sample Variables identified in this study Limits on constant targets in this survey Summary of variable sources Summary of constant sources Variability frequency Summary of Persistence Results Variability frequency from Wilson et al. (2014) Variability frequency from Radigan et al. (2014) Light curve system parameters for HAT-P-1b System parameters for GJ 1214b a xvi

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19 Declaration of Authorship Work presented in 3.1 has been published in the Astronomy & Astrophysics journal with the title: The brown dwarf atmosphere monitoring (BAM) project. I. The largest near-ir monitoring survey of L and T dwarfs, 2014, A&A, Volume 566, p I obtained the data, lead the analysis of the work, and wrote the paper in colaboration with Abhi Rajan and Prof. Jenny Patience. I developed the software used in the analysis and was responsible for the analysis and interpetation of the results. Credit: Wilson, P. A., Rajan, A. & Patience, J., reproduced with permission, c ESO. Work presented in 4.1 is work in preparation and will be submitted to Monthly Notices of the Royal Astronomical Society with the title: Detection of potassium in HAT-P-1b from narrowband spectrophotometry. I wrote the paper, performed the analysis and intepretation of the data under the supervision of Prof. Frédéric Pont and Dr. David Sing. Credit: Wilson, P. A., Sing, D. K., Nikolov, N., Pont, F., Fortney, J. J., Ballester, G. E., López-Morales, M., Vidal-Madjar, A., Désert, J.-M. and Lecavelier des Etangs, A. Work presented in 4.3 has been published in published in Monthly Notices of the Royal Astronomical Society with the title: A search for methane in the atmosphere of GJ 1214b via GTC narrow-band transmission spectrophotometry, 2014, MNRAS, Volume 438, Issue 3, p I wrote the paper, performed the analysis and intepretation of the data under the supervision of Dr. David Sing. Parts of the data reduction was done in collaboration with Colón, K. D. Credit: Wilson, P. A., Colón, K. D., Sing, D. K., Ballester, G. E., Désert, J.-M., Ehrenreich, D., Ford, E. B., Fortney, J. J., Lecavelier des Etangs, A., López- Morales, M., Morley, C. V., Pettitt, A. R., Pont, F., Vidal-Madjar, A. xviii

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21 Abbreviations ADU AU BAM BD CNO CTIO CMD DIT E-ELT EGP GTC HST IMF IR JWST MCMC MKO NDIT NGTS NOT NTT OSIRIS SED Analogue to Digital Unit Astronomical Unit Brown dwarf Atmosphere Monitoring Brown Dwarf Carbon Nitrogen Oxygen Cerro Tololo Inter-American Observatory Colour Magnitude Diagram Detector Integration Time European Extremely Large Telescope Extrasolar Giant Planet Gran Telescopio Canarias Hubble Space Telescope Iitial Mass Function Infra Red James Webb Space Telescope Markov Chain Monte Carlo Mauna Kea Observatories Number of Detector Integration Times Next-Generation Transit Survey Nordic Optical Telescope New Technology Telescope Optical System for Imaging and low-intermediate-resolution Integrated Spectroscopy Spectral Energy Distribution xx

22 Abbreviations xxi SofI TESS TTV Son of Isaac Transit Exoplanet Survey Satellite Transit Time Variation

23 Physical Constants Atomic mass unit m u = kg Boltzmann s Constant k = J K 1 Planck s Constant h = J s Speed of Light c = m s 1 Stefan-Boltzmann Constant σ = 2π5 k 4 15c 2 h 3 = J K 4 m 2 s 1 xxii

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25 Dedicated to my father, Anthony Berry Wilson, who made my dream of becoming an astronomer possible. xxiv

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27 Chapter 1 Introduction 1.1 Brown Dwarfs Definition Brown Dwarfs (BDs) are regarded as sub-stellar objects with a mass ranging from about 73 times that of Jupiter (M Jup ) down to a few Jupiter masses. The upper mass boundary dividing BDs from stars is well defined and set at the hydrogen burning limit, whereby an object with a central temperature insufficient for sustained hydrogen fusion in its core is considered a BD. Without hydrogen fusion in the core, thermal equilibrium is never reached and the BD steadily cools with time. The boundary between BDs and planets is currently unclear and is still a subject of much debate with no IAU official definition 1. Numerous studies have used the deuterium burning limit as a lower BD limit, whereby an object is no longer able to fuse deuterium in its core. For a solar metallicity object, the lower limit for deuterium burning is 13 M Jup (Burrows et al. 2001). The deuterium burning limit however, is dependant on a number of different factors such as the objects helium abundance, the initial deuterium abundance as well as the metallicity of the object (Spiegel et al. 2011). More importantly there is no robust physical justification for this limit. It has been suggested that the overlapping BD and planet regimes should be distinguished by their formation mechanisms (Chabrier et al. 2014), with planets forming via core accretion in protostellar discs and BDs akin to stars which form in molecular clouds. For the remainder of this thesis, 1 1

28 Introduction 2 the formation based distinction will be used to differentiate BD from exoplanets. Differentiating between the two formation scenarios observationally remains a challenge as observations are difficult to constrain. One way of differentiating between the two formation mechanisms is by studying the composition of the object. If the object has formed through disk instabilities it will have a chemical composition similar to the original star forming material, whereas if it formed via core accretion it may be enhanced or depleted in some elements. The limiting factor for spectroscopically differentiating between the two scenarios are spectral resolution and signal to noise which are ultimately governed by the brightness of the object. The high resolution observations are further limited to young self luminous objects with wide enough separations from their host star to allow for spectroscopic observations. Observations of HR 8799C, a 10 M Jup (Marois et al. 2008) planet, by Konopacky et al. (2013) found an enhanced C/O ratio together with an under abundance of C and O in the atmosphere of HR 8799C compared to its host star. These results favour a core accretion scenario although, as the authors suggest, the results are subject to caveats related to planet migration and chemical evolution history which are unknown. Mean density measurements can also give important clues to the formation history of low mass objects within the exoplanet / BD mass regime. A measured radius which is significantly smaller than what is expected for a near solar metallicity object can indicate an enhanced abundance of heavy elements in favour of the core accretion scenario. The opposite is not necessarily true as a larger than expected radii does not necessarily mean there is an under abundance of heavy materials (Leconte et al. 2009), but could instead be due to a radius inflation which is observed in many hot-jupiter atmospheres (Bodenheimer et al. 2003; Burrows et al. 2007; Charbonneau et al. 2000). Hot-Jupiters, jovian planets on close orbits to their host star, will be discussed in Detection Techniques There are three techniques currently used to discover BDs, which depend on the properties of the BD itself. One of the most straightforward techniques is the direct detection of an object outside the luminosity and effective temperature domain occupied by stars. This is the case for old BDs, but not for young BDs ( 100Myr), who frequently occupy the luminosity and effective temperature domain of the very low-mass stars (VLMS). To successfully distinguish young BDs from a VLMS, it

29 Introduction 3 is necessary to acquire spectra and look for signatures of youth, or to obtain proper motions to confirm the membership to a nearby association and from that infer the age. Obtaining spectra are not only important for finding signatures of youth, but also because by obtaining the spectral type one can constrain the temperature and mass of the object. It is common practice to use both optical colour magnitude diagrams coupled with proper motion measurements for initial identification of possible group members. Wide field photometric and astrometric surveys are commonly used to confirm if the BD candidate is a part of a association or not (e.g. Faherty et al. 2009; Pinfield et al. 2014). In the most ideal case one would obtain spectral signatures of youth coupled with measurements of distance (via parallax), proper motion and radial velocity. Quite often only a subset of the aforementioned properties are required for determining membership. The last technique used in detecting BDs is through dynamical interactions with other objects (e.g. binary systems), where orbital dynamics suggest a mass below the stellar minimum mass Brown Dwarf formation and evolution Stars are formed from molecular clouds which collapse under self gravity, forming cloud cores which eventually become dense enough to trigger sustained hydrogen fusion. Planets on the other hand, form in circumstellar disks, whereby gas accretes onto rocky cores. BDs (both free floating and companion BDs) do not have a universally accepted formation mechanism. The formation of BDs as scaled down versions of stars (e.g. Elmegreen 1999) and through instabilities in circumstellar disks akin to other stars and planets (e.g. Pickett et al. 2000) are both regarded as viable theories. In the first scenario, a BD could form if the star formation process was aborted before the onset of hydrogen burning. One such example is the ejection of a stellar embryo from small newborn multiple systems (Boss 2001; Reipurth & Clarke 2001) which could go on to producing self gravitating objects with masses down to 1 M Jup. For this scenario to happen, the ejection has to occur on a timescale less than the dynamical timescale of the parent core (on the order of 10 5 years), and the distance between the embryos has to be a few orders of magnitude smaller than the parent core. The hydrogen burning limit could also be avoided without the ejection of a stellar embryo. In the presence of a forming stellar cluster, BDs could form out of the

30 Introduction 4 filaments in the molecular gas which form due to the local self-gravity of the molecular gas and the gravitational potential of the cluster. In this case any subsequent accretion is stopped by the tidal sheer and high velocity dispersion present within the cluster (Bonnell et al. 2008). In star forming regions, OB stars deplete their surrounding area with their photoionizing radiation. Pre-existing protostellar cores in the vicinity of such stars could therefore have their accretion halted by removal of their envelope and surrounding disk (Whitworth & Zinnecker 2004). This is unlikely to be a dominant effect as the initial mass function (IMF) remains largely unchanged even in the presence of O stars (Luhman 2012). Turbulent fragmentation, whereby supersonic turbulence fragments the molecular cloud into dense sheets, filaments and cores over a wide range of masses, could also lead to the formation of cores small enough to produce BDs (Hennebelle & Chabrier 2008; Padoan & Nordlund 2002). In the second scenario, whereby BDs form more akin to planets, unstable circumstellar disks of high mass that surround stars can produce low mass companions which are later ejected by dynamical interactions (Bate et al. 2002). Stellar density (Taurus) compared to clusters with higher density (Trapezium) have been shown to have similar BD to star ratios, indicating that dynamical interactions may not be essential in forming BDs (Kroupa & Bouvier 2003). There are a number of observations which can be used to distinguish between the different formation models such as the shape of the low-mass IMF function (e.g. Chabrier et al. 2014), stellar multiplicity and kinematic distributions (e.g. Joergens 2006a; White & Basri 2003). However, different models often predict similar properties such as a low binary fraction amongst BDs and similar velocity distribution between stars and BDs making it particularly hard to distinguish between the different scenarios and therefore they are still very much a topic of debate. As BDs age, they cool, releasing the gravitational and internal energy generated during the earliest stages of their evolution. BDs with masses greater than M will undergo deuterium burning in their core, however, this phase of the evolution is short lived and typically does not last longer than 20 Myr (Baraffe 2014). The BDs with the highest effective temperatures are both young ( 100 Myr) and have masses close to the hydrogen burning limit ( 73 M Jup ), which combined result in a spectral type M6. Following the models of Burrows et al.

31 Introduction M 3000 M 0.1 M Effe ctive Te mpe rature (K) L 0.01 M M 0.05 M M 1000 T M Jup log 10 (Age ) (Gyr) Figure 1.1: Effective temperature vs age for objects with masses ranging from 1 M Jup to 0.2 M. The horizontal dashed lines represent typical upper and lower bounds of the M, L and T spectral types. Since BDs are not capable of sustained deuterium fusion, they steadily cool whilst stars, capable of hydrogen fusion, achieve a stable effective temperature. The models are from Burrows et al. (1993). (1997) and Baraffe et al. (1998) these BDs have an effective temperature 3000 K, which fall within the temperature regime of older M-dwarf stars. Compared to an M-dwarf star, the young BDs are both lower in mass and also have a larger radius (Gray & Corbally 2009) as they are still contracting to their final radius, roughly the size of Jupiter. As a result, young BDs exhibit a lower surface gravity compared to other BDs. The difference between BDs and M-dwarfs are clearly seen through their evolutionary tracks in Fig 1.1 where stars (top curves) achieve stable nuclear burning (thermal equilibrium) and thus stop cooling. In the case of BDs, only hydrostatic equilibrium is reached with radiation continuously escaping the upper atmosphere (photosphere). All stars at the substellar boundary together with BDs are thought to be fully convective causing the surface material to be efficiently mixed into the core. Since the temperatures required for sustained hydrogen fusion have to be greater than

32 Introduction K (Nelson et al. 1993) which is only slightly higher than the temperatures required to burn Lithium K (Pozio 1991), lithium may be used as an indicator of hydrogen fusion in the core. Unlike low-mass stars and those BDs with a greater mass which burn lithium during the early stages of their evolution, BDs with masses less than 0.06 M never reach the core temperatures necessary to burn lithium providing a robust test to distinguish the two objects. Young BDs in open clusters can aid in the determination of the age of the open cluster as well as the BDs themselves as they are assumed to have the same age as the cluster. The presence of lithium as a function of mass allows an age determination to be made of open clusters (where the stars and BDs are young). The boundry where lithium is no longer seen in the spectra (the lithium depletion boundry) depends on the age of the open cluster with the boundry migrating towards lower masses as the cluster age increases (corresponding to later spectral types) (Dobbie et al. 2010; Rebolo et al. 1992). Another way of distinguishing between low mass stars and BDs is to perform dynamical mass measurements. A BD low-mass star or BD - BD binary pair would be suitable for this sort of measurement. Using astrometric and spectroscopic measurements the dynamical mass of each component can be determined allowing the confirmation of BDs without being bound to any theoretical assumptions other than gravity (Zapatero Osorio et al. 2004). Therefore, low-mass binaries can provide excellent benchmarks with which to test models of ultracool atmospheres and inferred structure Characterising BD Atmospheres Spectral features of L,T and Y dwarfs The spectral energy distribution (SED) of a BD is primarily governed by the effective temperature, which depends mainly on the mass and age of the BD. As the BD cools the peak of the SED steadily moves redwards. For the most part, the SEDs are characterised by large molecular absorption bands. This is seen in Fig. 1.2 where the SED of a M8 dwarf star together with two BDs with spectral type T0 and T8 are shown with the most prominent atomic and molecular features labeled.

33 Introduction FeH Na I K I H 2 O VB 10, M8 (IR) 2MASSW J , L6±2 (IR) 2MASS J , T0 (IR) 2MASS J , T8 (IR) 1.5 Normalized Flux 1.0 TiO VO TiO CH 4 CO CH CH Wavelength (µm) Figure 1.2: The spectral standards VB 10 (M8), 2M0423 (T0) and 2M0415 (T8) shown with various different atomic and molecular bands. Identification done with the help of figures in (Burgasser et al. 2008, 2004). The spectra are from the SpeX Prism Spectral Libraries maintained by Adam Burgasser ( The hallmarks of M-type spectra are the optical signatures of TiO molecular bands with VO bands growing in prominence towards later spectral types. The neutral alkali metals Na I and K I are also prominent. For the later M-types (later than M6) the formation of dust weakens the molecular line absorption and contributes significantly to the overall continuum opacity. The species which start to condense are corundum (Al 2 O 3 ), perovskite (CaTiO 3 ) and other Al, Ti and Ca bearing molecules, iron (Fe), enstatite (Mg 2 SiO 3 ) and fosterite (Mg 2 SiO 4 ) (Burrows & Liebert 1993; Jones & Tsuji 1997; Lodders & Fegley 2002; Tsuji 2002) with the latter two molecules typically condensing at the transition between M-type and L-type brown dwarfs. The spectra of early L-type BDs are similar to older low-mass dwarf stars with a SED rich in atomic and molecular bands. The strong features caused by TiO and VO disappear whilst the neutral alkali lines such as Na I, K I persist together with

34 Introduction 8 the much less abundant Rb I and Cs I lines and occasional Li I for the younger L s as well as the hydride bands CrH, FeH and CaOH (Kirkpatrick et al. 1991; Lodders & Fegley 2002). The early L-type objects mark the changeover from CO to CH 4 as the main carbon bearing molecule, whilst the oxides are converted to hydrides with the alkali lines increasing in strength with the Na I and K I line wings dominating much of the optical spectrum. It is only for the latest L-types that the hydrides loose their strength with water features starting to increase in strength. Hot-Jupiter exoplanets have similar temperatures and many of the atmospheric signatures seen in L-dwarfs are also seen in exoplanets e.g.: Na I and K I (Charbonneau et al. 2002; Jensen et al. 2011; Sing et al. 2011) and H 2 O (Knutson 2007). The similarities and differences between BDs and exoplanets are discussed in more detail in 1.2. Moving into the domain of the early T-type BDs, a further deepening of the water bands is observed with the introduction of CH 4 absorption. By the end of the T- type sequence, water and CH 4 molecules completely dominate the spectrum giving the late T-types their characteristic three peaked shape in the near-ir. The subclasses associated with Y-type dwarfs have not yet been well defined. From the spectra obtained thus far, Y-dwarf spectra inherit many of the same traits as the late T-dwarfs. The emergence of ammonia features have been proposed as a trigger for Y-dwarfs, which are expected to belong to the temperature regime T eff 500 (Cushing et al. 2011; Lucas et al. 2010). Tentative detections of ammonia have been seen in high resolution spectra of Y-dwarfs although more observations are required to confirm the detection (Burrows et al. 2003; Cushing et al. 2011). As Y-dwarfs emit most of their flux at mid-ir wavelengths, the classification of the Y-dwarf subclasses will likely occur when this wavelength range is more readily accessible. Mid-IR observations from the ground are hard due to the interfering heat flux from Earth s atmosphere and currently there are no spaced based missions capable of mid-ir observations. The mid-ir capabilities of the James Webb Space Telescope (JWST) will be suitable for the continued development of a Y-dwarf classification scheme (Cushing et al. 2011). In summary, M-dwarfs are characterised by their strong TiO absorption bands. L-dwarfs are defined by the metallic oxides (e.g. TiO/VO) being replaced by metallic hydrides (CrH,FeH and CaOH) and neutral alkali metals (e.g. Na I, K I). T-dwarfs are defined by the onset of CH 4 absorption and show deeper H 2 O

35 Introduction 9 absorption bands. The Y-dwarfs discovered to date have similar SEDs to T- dwarfs, but show tentative signatures of NH 3 absorption bands which might very well define this class of objects. No universally accepted classification scheme for Y-dwarfs currently exists.

36 Introduction Chemistry and Composition The observed spectra described in the previous subsection, are dependant on the elemental composition and how these elements chemically react under different temperatures and pressures. BDs provide the ideal environment for the emergence and dissipation of condensate clouds, which govern the atmospheric chemistry and dominate their emergent spectra. The presence of clouds can have profound effects on the opacity of the atmosphere as well as alter the pressure-temperature profile and albedo. Clouds form through the condensation of condensible species present in the atmosphere. The efficiency of this process will depend on the nucleation process, which is the first stage of cloud formation allowing condensation to take place. There are two nucleation processes which occur in the atmospheres of BDs. The first, homogeneous nucleation, occurs when the partial pressure of a certain species in its gas phase exceeds its saturation vapour pressure. The condensation happens as a result of chance collisions between the molecules of the super saturated vapour, and is favoured when the concentration of condensation nuclei is low. An example of a homogeneously nucleating species is iron, one of the most refractory 2 elements present in the atmospheres of early-l type BDs. The second nucleation process is heterogeneous (or chemical) nucleation which occurs when nuclei are formed on pre-existing surfaces (different from the condensing species) which lowers the level of supersaturation required for nucleation to begin. Heterogeneous nucleation occurs when the partial pressure of a certain species in its gas phase exceeds its heterogeneous condensation pressure (instead of its saturation vapour pressure). Examples of heterogeneous nucleation from Earth include the formation of water clouds which occur as the result of condensation of water gas into water droplets via the nucleation of dust, sea salt and pollen suspended in the atmosphere (Marley et al. 2013). The atmospheres of L-dwarfs consists of hot dust grains of iron, silicates (solids containing Si-O groups) and oxides (at least one oxygen atom and one other element). These refractory condensates initially form at temperatures below T eff 3000 K in the atmospheres of M-dwarfs. The newly formed dust condensates present in the photosphere, absorbs the heat coming form the interior of the BD, causing the temperature to rise and the dust to sublimate. This processes repeats 2 Highest equilibrium temperatures (opposite of volatile).

37 Introduction 11 itself until T eff < 2800 K at which point chemical equilibrium is reached (Tsuji et al. 1996). The dust cloud layer which forms remains optically thin until the M-dwarf photosphere reach temperatures T eff < 2600 K (equivalent to M6 dwarfs Rajpurohit et al. 2013) where the impact of dust clouds on the SEDs become significant (Allard et al. 2013). In a static atmosphere, the formation of dust grains will continue and eventually become too heavy to stay suspended in the photosphere and subsequently they rain out. However, due to the dynamic nature of BDs atmospheres, convection will keep the dust suspended high in the atmosphere at lower temperatures. This suspension of dust results in a greenhouse effect which gives the L-dwarfs their characteristic red colour. The dust in the atmospheres of late-m and L-dwarfs also results in Rayleigh scattering which acts as the dominant opacity source throughout the visible part of the spectrum (Allard et al. 2012). The efficiency of the dust settling will depend on the T eff and surface gravity of the BDs, and has a direct impact on the emergent flux (see for models which incorporate this sedimentation efficiency). Inevitably the temperature will become sufficiently low for a transition from a dusty to a clear atmosphere to occur, which occurs at the transition between the L and T spectral types (see ). Chemical equilibrium models are used to predict which species are expected to condense out of the atmosphere at a given temperature and pressure. Fig. 1.3 shows a variety of condensation equilibrium curves for species expected to condense in the atmospheres of BDs (dashed lines). These lines show the pressure and temperature conditions necessary for condensation to occur. The solid curves are model atmospheres of various temperatures. Cloudless models are shown in blue, with orange and red curves representing a sedimentation efficiencies of f sed = 4 and 2 respectively. For L-type BDs ( K, Kirkpatrick et al. 1999; Martín et al. 1999), dust clouds of corundum (Al 2 O 3 ), iron (Fe), fosterite (Mg 2 SiO 4 ) and enstatite (MgSiO 3 ) dominate. For T-type BDs ( K) a variety of condensates are expected to form such as Cr, MnS, Na 2 S, ZnS and KCl (Morley et al. 2012). These sulfide and salt clouds are expected to condense in mid- to late T-dwarfs, likely resulting in photometric variability (Morley et al. 2014). As a result the first searches for variability for late-type BDs are under way (Rajan et al. 2014). For the coolest BDs known to date 3, the Y-dwarfs, water (H 2 O) and ammonia (NH 3 ) are expected to condense. This happens at temperatures of T eff The coldest BD known to date has a temperature of T eff 250 K (Luhman 2014).

38 Introduction 12 3 log(pressure) (bar) NH 4 H 2 PO 4 H2 O 400 K ZnS KCl Na 2 S 600 K 900 K MnS 1300 K Cr MgSiO 3 Mg 2 SiO 4 Fe Al 2 O Temperature (K) Figure 1.3: Pressure-temperature profiles of model atmospheres showing cloudless models (blue) and models with f sed = 4 (orange) and 2 (red). The thicker lines represent the 1 6 µm photosphere. Adopted from (Morley et al. 2012) and used with permission from C. Morley. 375 K for water and T eff 200 K for ammonia (Morley et al. 2014). Given data on the composition and abundance of various species (often assumed solar), and armed with a chemical equilibrium model such as Burrows & Sharp (1999), the equilibrium composition of the atmosphere can be obtained. This is done by calculating which chemical species are thermodynamically favoured by minimizing the Gibbs free energy of the system (Cooper et al. 2003). Once the chemical species have been determined, their particle size distribution and number densities above the base of the cloud are computed. The methodological approach used in these calculations varies between the model atmospheres and are discussed in more detail in Regardless of the models used, it is important the properties of the cloud be taken into account when computing the chemical equilibrium of the atmosphere. This is not only due to the influence of clouds on atmospheric temperature and the emergent flux, but because once a species has condensed, it is no longer available to react at lower temperatures and pressures higher up in the atmosphere (Marley et al. 2013).

39 Introduction 13 As it is the gas in the atmosphere which provides the atoms and molecules needed for the condensation processes to take place, the composition of the gas plays an important role in cloud formation (liquid and solid) and the chemistry of BD atmospheres. At temperatures below 1300 K methane becomes the dominant carbon bearing molecule rather than CO. This leads to the emergence of the methane clouds, greatly affecting the flux received in the H and K bands (Burgasser et al. 1999; Geballe et al. 2002; Leggett et al. 2000). The conversion between CO and CH 4 proceeds according to the following thermochemical reaction, CO(g) + 3H 2 (g) CH 4 (g) + H 2 O(g) (1.1) under the assumption of chemical equilibrium. Carbon is preferentially in the form of CO at higher temperatures deep in the BD atmosphere, whereas CH 4 is more stable thermodynamically in the upper atmosphere where the temperature is lower (Lodders & Fegley 2002). The convective nature of BD means vertical mixing takes place, which causes an upwelling of CO from the deep atmosphere to the upper atmosphere, as observed in Jupiter (Prinn & Barshay 1977). This causes an overabundance of CO compared to that which equilibrium predicts as the double bond between the carbon and oxygen atoms make the conversion back to CH 4 very slow (Fegley & Lodders 1996; Seager 2010). The same sort of chemical disequilibrium happens to molecular nitrogen (N 2 ), which is the preferred state of nitrogen at hotter temperatures and ammonia (NH 3 ), which dominates at lower temperatures. The net thermochemical reaction N 2 (g) + 3H 2 (g) 2NH 3 (g) (1.2) proceeds more slowly to the right due to the strong triple bond in N 2. Although the effects of disequilibrium chemistry are well known, and despite disequilibrium chemistry being a mature field (Barshay & Lewis 1978; Fegley & Prinn 1985; Lodders & Fegley 2002), predicting the abundances of various elements and molecules as well as their particle size distribution becomes hard due to the dependence on atmospheric parameters such as temperature and vertical mixing.

40 Introduction Variability at the L-T transition As BDs age, and as a result cool with time, their atmospheres undergo a plethora of physical and chemical changes. Nowhere along the BD spectral sequence are these changes so abrupt as at the L-T transition. The transition itself is marked by a rapid change in near-ir colours from red to blue (J K 2.0 mag) over a narrow temperature range ( T eff K) resulting in a brightening in J-band ( 1 mag). A colour magnitude diagram (CMD) of BDs at various temperatures show the colour transition (Fig. 1.4, left) and the J-band brightening (Fig. 1.4, right). L-type BDs (shown as circular points in Fig. 1.4), owe their red colour to the reradiation of heat absorbed by the high opacity of the dust clouds in the upper atmosphere. The T-dwarfs on the other hand (diamond points in Fig. 1.4), have clear atmospheres with the dust having condensed out below the observable photosphere, allowing flux from deeper and hotter layers to emerge which are both bluer and brighter at near-ir colours. Understanding the causes behind the change from a dusty to a clear atmosphere is one of the outstanding problems of BD evolution. One theory is that the dynamical state of the atmosphere changes due to different sedimentation efficiencies, leading to the sudden disappearance or clearing of condensate clouds (Knapp et al. 2004; Saumon & Marley 2008). Tsuji & Nakajima (2003) using the unified cloudy models of L and T dwarfs, proposed that the blue ward shift in J-K colours and brightening in the J-band was due to the migration of a thin dust cloud from the optically thin (τ < 1) to the optically thick (τ 1) inner region of the photosphere. Instead of being an evolutionary effect, the J-band brightening could be explained by BDs with varying surface gravities and ages. Observations of flux reversal binaries (binary systems where the later type binary is brighter in J and fainter in H and K s ) has since discounted this theory. Since the flux reversal binaries are presumably formed at the same time, wast differences in ages and surface gravities between the two binaries components can be ruled out. This indicates that the brightening seen between late-l to early T-type objects are an intrinsic property of the objects and not a selection effect (Gelino et al. 2014). The change from a dusty to a clear atmosphere also induces changes in the observed flux on timescales comparable to the rotation rate of the BD which are likely due to variations in cloud thickness. This breakup in clouds, also referred to as the patchy cloud hypothesis, has been suggested by (Ackerman & Marley 2001; Burgasser

41 Introduction HD 44627b HD 44627b 14 M J (mag) 16 2M1207b 2M1207b J K (mag) M6 M8 L0 L2 L4 L6 L8 T0 T2 T4 T6 T8 Y0 Y2 Spectral Type Figure 1.4: Absolute MKO J magnitude as a function of J K colour (left). The symbols are representative of BDs with spectral type M (triangles), L (circles), L-T transition L7-T4 (squares), T (diamonds) and Y (crosses). Absolute MKO J magnitude as a function of spectral type (right), showing the J band brightening at T2-T5. The two planet candidates HD 44627b and 2M1207b are labelled highlighting the similarity between BDs and planets by allowing both objects to be placed in the same CMD. The data is a compilation of various studies available at the Database of Ultracool Parallaxes maintained by Trent Dupuy. et al. 2002; Folkes et al. 2007). There is a growing body of evidence supporting the patchy cloud hypothesis from photometric variability studies showing periodic variations possibly caused by partial cloudiness and cloud thickness variations (e.g. Apai et al. 2013; Artigau et al. 2009; Radigan et al. 2012). Observations using Doppler imaging techniques have also shown large-scale features indicative of patchy clouds (Crossfield et al. 2014). Variability might also be caused by the coupling of clouds to the global atmosphere circulation (Showman & Kaspi 2013; Zhang & Showman 2014), with the variability emerging as a consequence of thermal perturbations emitted from deeper layers within the brown dwarf atmosphere (Robinson & Marley 2014).

42 Introduction 16 Results from a large near-ir photometric monitoring campaign which was aimed at quantitatively determining the level and frequency of variability across a uniform and unbiased sample of 69 ultracool L & T type BDs (Wilson et al. 2014) are presented in 3.1. One of the main results to emerge from this survey was that the frequency of variables across the L-T transition is indistinguishable from earlier or later spectral types. This may suggest the early onset of cloud condensation of mid-l dwarfs and the emergence of sulfide clouds in mid-t dwarfs (Morley et al. 2012). It could also be that the patchy cloud scenario may not be the only source of variability with thermal perturbations being a possible candidate for variability.

43 Introduction The Exoplanet-Brown Dwarf Connection The Shared Parameter Space BDs and hot-jupiter exoplanets frequently overlap the same parameter space with comparable radii, effective temperatures, composition and surface gravities. Furthermore BD and exoplanet observations compliment each other. BDs are generally easier to characterise as they can be observed in isolation (in the absence of a host star) and because they are in most cases more luminous than exoplanets. Exoplanets on the other hand allow us to further extend the probable parameter space, such as to lower pressures. Despite an overlap in several parameter spaces, the two types of objects can differ significantly in detail. Below follows a comparison between some of the most important characteristics between the two types of objects Comparison of mass From the discussion of the definition of a BD in 1.1.1, it is clear that without a universally accepted definition, it is to be expected that the mass regimes of low mass BDs and high mass exoplanets will overlap. For isolated BDs, the mass estimates are generally not as accurate (especially if the age is not well constrained) when compared to exoplanets which orbit a host star allowing for dynamical mass measurements to be made. The overlap in mass can bee seen in the mass-radius diagram shown in Fig Comparison of radii Stars on the main sequence maintain hydrostatic balance when their gravitational potential energy equals two times their thermal energy and be expressed as GM 2 /R (M/m p )kt nucl. As such the radius of a star is proportional to its mass, R M. This relationship remains constant due to the fusion temperature of hydrogen at a constant K (the exact value depends on density) and persists as long as the fusion of hydrogen to helium occurs via the proton-proton chain (as opposed to the CNO cycle). Young BDs, follow a similar mass-radius relationship as stars. This is due to the young BDs having a larger radii as they

44 Introduction 18 are still contracting from their formation, and for those with a greater mass, these might still be burning deuterium. The gravitational potential energy of BDs are partially supported by electron degeneracy pressure. The Pauli exclusion principle states that two identical fermions (in this case electrons) can not occupy the same quantum state. Therefore when the the lower energy states become occupied, the electrons have to move to higher energy states which contributes to the degeneracy pressure. This temperature independent pressure inhibits the BDs from contracting further. For a fully degenerate object (such as a white dwarf), an equilibrium is reached when the gravitational potential energy, E p GM 2 /R, is balanced by the kinetic energy, E k M 5/3 /R 2. This results in a radius which scales with mass as R M 1/3. BD dwarfs and hot-jupiters, are however only partially degenerate in their core and Coloumb pressure plays a significant role in the hydrostatic balance. The electron degeneracy is strongest for those BDs with a larger mass, taking on a mass-radius relation of about R M 1/8 (less than the fully degenerate case R M 1/3 ). For objects with a lower mass, the Coloumb pressure (constant density, R M 1/3 ) becomes ever more significant. When the Coloumb pressure (R M 1/3 ) and the degeneracy pressure (R M 1/3 ) become similar in magnitude (R M 0 ) (Burrows et al. 1993; Oppenheimer et al. 2000) a flattening in the mass-radius relation is seen for BDs with a lower mass and hot-jupiters as shown in Fig For planetary mass objects Coloumb pressure dominates. Coloumb pressure, which is caused by the electromagnetic repulsion between the electrons of one molecules from those of another is characterised by a constant density. It follows from the constant density (ρ M/R 3 ) that the radius scales as R M 1/3. Neptunian and Super-Earths objects ( M Jup ) are found in this regime Comparison of surface gravities and pressures A natural consequence of BDs and hot-jupiters having similar radii and a partial overlap in the mass regime, is that their surface gravities also partially overlap. As the radii are almost constant amongst the two types of objects, the surface gravities depend strongly on mass. The overlap happens between the dense hot- Jupiters of high mass and the young low mass BDs. The surface gravities of BDs and Exoplanets is shown in Fig Hot-Jupiters typically have surface gravities

45 Introduction Young BDs Hot-Jupiters Stars Radius [RJup] 10 0 BDs Super-Earths Mass [M Jup ] Figure 1.5: Mass - Radius diagram showing the parameter space of stars (red star shaped markers) with data from Ségransan et al. (2003), field BDs (purple) and young BDs (orange) from the BD lists maintained by Wm. Robert Johnston and planets (open circles) with data from exoplanets.org. HAT-P-1b featured in 4.1 is shown amongst the hot-jupiters (blue), whilst GJ 1214b is shown amongst the super-earths (green). in the range m/s 2 whilst BDs in most cases have a larger mass and thus commonly have surface gravities times greater. Age also has an affect on surface gravity, with younger objects ( 100 Myrs) having larger radii as they are still contracting from formation. Surface gravities of BDs can be inferred from signs of youth present in their spectra. Weak pressure broadening leading to narrow alkali lines, enhanced metal oxide absorption bands and a triangular peaked spectrum in H-band are all signs of youth (Faherty et al. 2014). These spectroscopic signatures are however dependant on temperature and/or metallicity which results in degeneracies, which only loosely constrain the surface gravity (Rice et al. 2011). Transiting exoplanets on the other hand, have the advantage of accurate radii and mass measurements which allow the surface gravity to be determined directly. The affect of a larger surface gravity is higher photospheric gas pressures. Thus, in the case where a BD and an exoplanet have similar temperatures, the surface gravity will inevitably affect the temperature-pressure structure of the atmosphere. This has a direct effect on which species condense out of the atmosphere due to the resulting changes in partial pressure. The photospheric pressure can also directly

46 Introduction C69-Sub-003 Kepler-20 f LOri-SOC 11 CoRoT-27 b LOri-SOC 13 Kepler-39 b CoRoT-3 b Teff & Teq (K) log(g) (cgs) Figure 1.6: T eff (for BDs) & T eq (for Exoplanets) Vs. log(g). A number of BDs (purple pentagons) and exoplanets (blue circles) have overlapping surface gravities although BDs usually have higher surface gravities, a result of larger masses with radii similar to most hot-jupiters. The BD data is from lists maintained by Wm. Robert Johnston whilst the exoplanet data is from exoplanets.org affect the opacity of the atmosphere such as the width of the alkali lines through pressure broadening. Changes in pressure alter chemical reaction rates and lead to non-equilibrium effects such as the interplay between CO and CH 4 (described in the section on chemistry and composition, ). At the high temperatures and pressures present deep in the atmosphere, chemical reactions proceed faster, increasing the likelihood of reaching chemical equilibrium. However, as material is dredged up to parts of the atmosphere where the temperatures and pressures are lower, the timescale for chemical equilibrium, τ chem, becomes longer than the vertical mixing timescale, τ mix, which leads to disequilibrium chemistry. The mixing timescale τ mix at the radiative layer in the atmospheres of BDs and exoplanets is given as τ mix H 2 /K E, where H is the scale height (defined in ) and K E is the eddy diffusion coefficient. For the convective zone of the atmosphere

47 Introduction 21 τ mix H/v c, where v c is the convective velocity. In either case τ mix is dependant on the pressure scale height H, which varies with surface gravity which is linked directly to the pressure as P g/κ, where κ is the Rossland mean opacity. As such, the atmospheric pressure can also directly affect the equilibrium chemistry, despite similar atmospheric temperatures and composition Comparison of temperatures The atmospheric temperatures of both BDs and planets govern the chemical equilibrium of the atmosphere which directly affects the SED s and is thus one of the most important parameters when characterising their atmospheres. The heat present in BDs atmospheres comes from their interiors whilst hot-jupiters are also heated from above by their host star. Thus when comparing temperatures it is important to consider which sort of measure of temperature is discussed. The effective temperature, T eff, is the temperature of a blackbody which radiates the same total flux as the emitting object, in this case a BD or an exoplanet. It describes the global temperature of the object at the altitude where the bulk of the radiation leaves the object and is generally regarded as the temperature of the photosphere. This quantity can be determined for BDs either by fitting theoretical spectra to observed spectra or by bolometric luminosity (L ) measurements. For field-age L and T type BDs, their radii (R ) are fairly constant allowing a T eff estimate to be made using the Stefan-Boltzmann law, L = 4πR 2 σt 4 eff (1.3) where σ is the Stefan-Boltzmann constant. This can be done providing the bolometric luminosity is known. Hot-Jupiters are dominated by radiation from their host star. As such, no internal luminosity can be measured and since spectra most often are of low resolution and low signal to noise, measuring the T eff becomes very difficult. The exception to this are the directly imaged planets, where much higher resolution spectra are obtainable allowing T eff to be measured either using theoretical spectra (Lagrange et al. 2009) or atmospheric retrieval techniques (Lee et al. 2013). For planets, the thermal equilibrium temperature (T eq ) is typically calculated instead as a way of estimating T eff. The T eq is never measured directly as it is only a theoretical number. Using the principles of conservation

48 Introduction 22 of energy, whereby energy in the form of incident stellar radiation balances out the energy absorbed by the planetary atmosphere (an isothermal atmosphere) the relationship can be expressed as: L 4πRpσT 2 eq 4 = (1 A B )πrp 2 (1.4) 4πd 2 where R p is the radius and A B the bond albedo of the planet and the term L /4πd 2 is the energy per unit area per unit time at a distance d from the star. Equation 1.4 can be rearranged such that: T eq = 1 2 [ (1 AB )L πσd 2 ] 1 4. (1.5) Substituting Eq. 1.3 into Eq. 1.5 allows T eq to be calculated given the effective temperature of the host star, T eff. As it is only possible to observe one hemisphere at a time and since the stellar radiation is not uniformly distributed around the planet, such as for tidally locked or slowly rotating exoplanets, a correction factor, f, is used (Seager 2010). The relationship between T eq and T eff is expressed as ( ) 1 R 2 T eq = T eff [(1 AB )f] 1 4 (1.6) d where a perfect heat redistribution has f = 1/4 whilst in the case of no advection (no dynamical redistribution of heat) f = 2/3. Both the T eff and T eq have been measured for all the planets in our solar system and the two temperatures have been found to be constant within 15 K of each other. This precision is due to the accurate determination of the parameters in Eq For an exoplanet, the calculated equilibrium temperature will largely depend on how accurate the stellar properties (T eff and R ) are determined. T eff can be obtained by fitting synthetic model spectra to observations 4. R can be obtained through photometric or spectroscopic measurements with interferometry giving the most accurate values down to within 1% accuracy (von Braun et al. 2011). Regardless of the technique used to derive a radius, the distance 4 Stellar temperatures can also be obtained by photometric measurements in combination with theoretical colour-temperature relations (VandenBerg & Clem 2003).

49 Introduction WASP-12b Brightness Temperature, TB (K) WASP-3b CoRoT-1b HAT-P-1b WASP-4b OGLE-TR-113b CoRoT-2b WASP-43 TrES-3b TrES-2b WASP-19 T eq = T B K s -band ( µm) Equilibrium Temperature, T eq (K) Figure 1.7: Brightness temperature at K s wavelengths as a function of dayside equilibrium temperature (isotropic reradiation and A B = 0). The dashed red line shows the 1:1 relationship between T B and T eq which corresponds to f = 1/4. T B and T eq are from: HAT-P-1b (de Mooij et al. 2011), OGLE-TR-113b (Snellen & Covino 2007), WASP-43 (Wang et al. 2013), TrES-2b (Croll et al. 2010), CoRoT-2b (Alonso et al. 2010), TrEs-3b (Croll et al. 2010), WASP-4 (Cáceres et al. 2011), CoRoT-1b (Rogers et al. 2010), WASP-3b (Zhao et al. 2012), WASP-19 (K-band) (Gibson et al. 2010; Mancini et al. 2013) and WASP- 12 (Cowan et al. 2012). (via trigonometric parallax) has to be known. The orbital characteristics are required to obtain d and lastly an albedo has to be assumed. Eccentricity effects as well as large day/night temperature contrasts make the equilibrium temperature measurements of exoplanets a poor proxy for the photospheric temperature, and stellar irradiation can lead to the formation of a thermal inversion where the upper atmosphere is much hotter than the equilibrium temperature (see section on thermal inversions, 1.3.6). Not knowing the photospheric temperature leads to a multitude of possibilities for atmospheric structure as several elements can condense to form clouds. The only temperature we can measure for exoplanets (without model assumptions) is the brightness temperature, T B. This temperature is defined as the temperature a black body of similar size in thermal equilibrium would have if placed at the same distance away from the star as the exoplanet, and emitting the same flux within a specified wavelength range. Since the atmospheric opacity changes depending on the wavelength probed, it is important to state the wavelength the brightness temperature is measured at. Brightness temperatures have been measured for

50 Introduction 24 several planets both from space and the ground (see Fig. 1.7). Using a 1-D chemical code Venot et al. (2014) demonstrated that the brightness temperature of the sub- Neptune GJ 3470b could vary by a factor 2 at infrared wavelengths depending on the thermal profile used and the metallicity of the model. An increase in metallicity would increase the opacity, causing secondary eclipse measurements to probe higher in the atmosphere where the temperature is lower, giving a lower brightness temperature. In general a large difference between T eq and T B may suggest a poor energy redistribution. In the interest of comparing the atmospheric temperatures of exoplanets and BDs, great care must be taken, as temperatures are measured and/or calculated differently. For instance, T B is always greater than T eq, and neither are directly comparable to T eff as the measurements are fundamentally different and in some cases depend on the thermal profile and metallicity which are unknown Comparison of composition BDs have the clear observational advantage over exoplanets that they are in most cases not orbiting closely to a host star, often million times brighter at near- IR wavelengths, making observations a challenge. BD spectra can be obtained directly often covering a broader wavelength range and at much higher resolution. It is therefore no surprise that we have more direct detections of various species within their atmospheres. In the chemistry and composition of BDs were discussed with focus on how it changed primarily as a function of temperature. With exoplanets, especially closely orbiting hot-jupiter and super-earths which are tidally locked, the situation can be quite different, especially as there are two temperature regimes, a highly irradiated day side, and K cooler night side. This causes fast km/s winds (Snellen et al. 2010) which drive atoms and molecules from the dayside to the night side where they are expected to condense out. M- type and L-Type BDs show clear signs of TiO/VO in their spectra (see Fig. 1.2). Although many attempts have been made at detecting TiO/VO expected to be present in exoplanet spectra (Fortney et al. 2010), no clear evidence of TiO/VO has yet been found in exoplanet atmospheres. This strengthens the theory that TiO/VO might condense out on the night side of the planet, or get depleted via a cold trap (see section on thermal inversions, 1.3.6).

51 Introduction 25 The way in which spectra are obtained, generally differ from BDs and exoplanets, the exception being directly imaged planets on wide orbits, which allow spectra to be obtained directly (see section on direct imaging ). Transmission spectroscopy, a technique used to probe the atmospheres of exoplanets using transits (explained in detail in ), only probes the composition of the gas at the planet terminator, where the stellar light filters through the atmosphere. This occurs at low pressures (mbar to µbars), orders of magnitude lower than the pressures of the photosphere, which is observed when direct spectra of BDs are obtained. As such, the composition is only valid for the gas at the limb of the planet and at low pressures (mbar to µbars). The atmospheres of hot-jupiters contain many of the same constituents as BD atmospheres such as Na I (Charbonneau et al. 2002; Redfield et al. 2008), K I (Sing et al. 2011), CO, CH 4 (Swain et al. 2008) and H 2 O (Grillmair et al. 2008; Wakeford et al. 2013). The consequence of closely orbiting a host star has allowed for the detection of C II, O I (Vidal-Madjar et al. 2004), S III (Linsky et al. 2010) and Mg II (Fossati et al. 2010) in hot-jupiter atmosphers. Although C, O, S and Mg have all been detected in BD atmospheres, exoplanets have the advantage that they can be studied at ultraviolet wavelengths, which are not possible for BDs as they have no detectable flux at these wavelengths. Jupiter, Saturn, Uranus and Neptune all have metal 5 enriched atmospheres. For example, Jupiter has a 2 4 higher abundance of carbon, oxygen, nitrogen, sulphur and various noble gasses (Atreya et al. 2003) compared to solar composition. Saturn has a 10 solar abundance of carbon (Flasar et al. 2005) and an enhanced abundance of water and oxygen (Visscher & Fegley 2005). This enhancement of metals is likely the result of the core accretion formation mechanism, whereby the planets formed from within a protoplanetary disk rich in heavy elements. The core accretion model, which will be covered in more detail in has emerged as the dominant formation mechanism for exoplanets, so it is likely that exoplanets will also possess super solar abundances. BDs on the other hand are expected to have metallicities similar to stars, with the most metal rich BDs having abundances that generally do not exceed 3 5 solar abundances. For BDs in the metal poor thick disk and halo, their metallicities are expected to extend well below solar metallicites (Burningham et al. 2013; Mace et al. 2013; Pinfield et al. 2014). This difference in metallicities has a profound effect on the chemistry 5 Metals in this context means all elements heavier than H and He.

52 Introduction 26 and molecular composition of the atmospheres. Furthermore, the composition of the gas determines which species condense to form clouds. Chemistry and cloud formation has previously been discussed in

53 Introduction Exoplanets A brief overview There are infinite worlds both like and unlike this world of ours. For the atoms being infinite in number are borne on far out into space. Epicurus, BC An exoplanet is any planet which is not in our solar system. The prefix exo originates from Greek and translates into outside. Although exoplanets were thought to exist in ancient times, it was not until 1992 when the first confirmed discovery of an exoplanet, was made by Wolszczan & Frail (1992). They discovered two planets which orbited a 6.2 ms pulsar 500 pc away by studying timing variations using the biggest telescope in the world, the 305 m Arecibo radio telescope. The subsequent discoveries of exoplanets, notably the first detection of an exoplanet around a sun like star (Mayor & Queloz 1995), the first detection of a transiting planet (Charbonneau et al. 2000) and an exoplanet atmosphere (Charbonneau et al. 2002), used a range of techniques which will be described in more detail below. Thanks to a number of exoplanet surveys aimed at detecting exoplanets, and the subsequent follow-up studies aimed at characterising them, the first few steps to understanding these new worlds have been made. With exoplanets known to outnumber stars (Cassan et al. 2012), and with new powerful telescopes and instruments on their way (e.g., JWST, E-ELT) the future of exoplanet research has an exciting future ahead Detection techniques When it comes to detecting exoplanets, there are several techniques available at the disposal of the exoplanet hunter. Each technique, quite often sensitive to different types of planets, is briefly summarised below and shown in Fig Amongst these techniques the direct imaging and observations of transiting exoplanets have had the greatest impact on atmosphere characterisation and as such these methods will be discussed in more detail in the subsections below. The main techniques used to detect exoplanets are:

54 Introduction 28 Direct imaging: The exoplanet is imaged directly using large telescopes fitted with adaptive optics and coronagraphs. The technique is most sensitive to the warmer, bright (young) and massive exoplanets on wide and/or eccentric orbits (large sky projected separations, e.g. Marois et al. 2008). The separation from the host star allows for spectra to be obtained directly and allows for the direct measurement of the luminosity. Radial velocity: The exoplanet is detected by measuring the Doppler shift in the host star light, a consequence of the gravitational affects between the two bodies. The technique is most sensitive to exoplanets with a large mass orbiting close to their host star perpendicular to the plane of the sky. The radial velocity technique allows for a minimum mass (dependant on orbital inclination) to be calculated (e.g. Pepe et al. 2011). Transits: The exoplanet is detected by measuring a periodic decrease in the flux received from the host star, as a consequence of the exoplanet transiting in front of the host star (e.g. Charbonneau et al. 2000). The transiting technique is most sensitive to large exoplanets orbiting close to their host star stars and provides an accurate determination of the planetary radius relative to the host star. Microlensing: The exoplanet is detected by measuring characteristic light curve changes caused by changes in the lensing effect observed when a star with a planet passes in front of a distant star (e.g. Gaudi 2012). The technique is limited to distant one time events and by the lack of accurate determinations of the planet and orbit parameters. It is however a very valuable technique due to the lack of strong radii or mass biasses making it ideal for statistical population studies. Transit timing variations: The exoplanet is detected by observing a change in periodic phenomena due to the presence of an exoplanet. Examples include a change in transit time (known as TTV) of one planet, due to the presence of others in multiple planet systems (e.g. Holman et al. 2010) and pulsar timing (e.g. Bailes et al. 2011), where anomalous movement (measured at radio wavelengths) can be used to infer the presence of a planet.

55 Introduction Planet mass log(m Jup ) Radial Velocity Transit Timing Microlensing Direct Imaging Semi-major axis log(a[au]) Figure 1.8: Planetary mass (log(m Jup )) as a function of semi-major axis. The shapes represent the various detection techniques; radial velocity (red circles), transits (blue diamonds), timing (black downward triangle), microlensing (orange upward triangle) and direct imaging (green stars) Direct imaging Amongst the different detection techniques, direct imagining is the only technique which allows for the direct measurement of the exoplanet itself. Despite the basic principle behind directly imaging a planet, it is a notoriously difficult technique in practice. This is due to the the enormous luminosity contrast between the exoplanet and the host star and the small angular separation between the two bodies. At optical wavelengths, where the black body curve of the host star peaks, the brightness contrast is on the order of Towards longer wavelengths the situation improves as the black body curve of the planet peaks, whilst that of the host star diminishes, resulting in a more favourable contrast ratio of For this reason, direct imaging observations are done at near-ir to mid-ir wavelengths. The diffraction limit of a telescope is the minimum angular resolution before the the two objects observed can no longer be separated. The angular resolution, θ can be expressed as

56 Introduction 30 θ = 1.22λ D (1.7) where D is the diameter of the telescope and λ the wavelength at which the observations are done. To be able to directly image planets which orbit close to the host star, it is most favourable to use a telescope with a large mirror diameter and also observe at longer wavelengths. The technique is most sensitive to high mass (M 5 10 M J ), young ( 100 Myr) exoplanet systems on wide orbits ( 5 AU) and therefore complements the other techniques (especially the transit method and RV method) which are more likely to detect planets which orbit close to their host star. Unlike the transit and phase curve measurements (described in the next section), which are the only other methods capable of detecting an exoplanet atmosphere, the direct imaging method allows for photometric and spectroscopic observations across a range of wavelengths to be obtained directly. The wide orbits means the exoplanet atmospheres are not subjected to strong irradiation from the host star (see thermal inversions 1.3.6) nor influenced much by stellar activity (see 1.3.5). Directly imaged planets therefore occupy a lot of the same parameter space as BDs allowing comparisons to be made (see section on the exoplanet-bd connection, 1.2.1). An added benefit of wide orbits is that the observations are not time critical, a natural consequence of Kepler s 3 rd law The Transit Method When exoplanets pass in front of their host star (as seen from Earth), a portion of the start light is blocked out and a decrease in the photon flux is measured. Measuring the change in flux over time, allows for the creation of a light curve (see Fig.1.17). Fitting models to the light curve, various characteristics such as orbital motions and atmospheric composition can be extracted. Both the size of the host star and the planet will determine the decrease in flux during the transit. The orbital distance between the exoplanet and its host star does not affect the transit depth due to the enormous distance from Earth. The transit method is particularly useful for calculating the radius of an exoplanet. To first order (assuming the stellar disc is of uniform brightness, and neglecting

57 Introduction 31 a i b Figure 1.9: The impact parameter b varies from b = 0 centre of stellar disk with b = 1 being on the cusp of the disc. l b = a cos i/r* R* R * p Figure 1.10: Star-planet geometry showing the distance traversed by the planet, 2l, impact parameter of the system, b and the stellar and planetary radii, R and R p respectively. any flux from the planet) the ratio of the observed change in flux, F, to that of the stellar flux F can be expressed as: F F = R2 p R 2 (1.8) where R p and R are the planetary and stellar radii respectively. As described below, limb-darkening will have an affect on the transit light curve, but to first order, the equation above holds.

58 Introduction 32 i B 2l A a Figure 1.11: The orbital geometry of a transiting exoplanet system showing the projected distance travelled across the surface of the star, 2l, between the points A to B and the angle α this geometry forms, with the inclination, i, and semi major axis, a, shown. Impact Parameter: The total transit duration is heavily dependent on the impact parameter b, which is defined as the sky-projected distance between the centre of the stellar disc and the centre of the planetary disc at conjunction 6 and is shown in Fig Assuming a circular orbit the impact parameter is expressed as: Transit Duration: b = a cos i R. (1.9) The total transit duration, T dur, defined as the time during which any part of the planet obscures the disc of the star, depends on how the planet transits the host star. If the exoplanet crosses the centre of the stellar disc (b = 0), the transit duration is the longest with b 0 signifying a shorter transit duration. With the help of Fig and using Pythagorass theorem, the length the planet has to travel across the disk of the star can be expressed as, 2l = 2 (R + R p ) 2 b 2. (1.10) 6 Conjunction: The point in the orbit where two objects are most closely aligned, as viewed from Earth. 7 The figures and derivations are adapted from Transiting Exoplanets, by Carole A. Haswell.

59 33 Introduction Figure 1.12: Limb darkening of a star showing how the intensity and temperature diminishes as an observer looks towards the limb of the star. With the aid of Fig. 1.11, the exoplanet moves from A to B around its orbit, creating an angle α (measured in radians) with respect to the centre of the host star. With the assumption of a circular orbit, the distance around an entire orbit is 2πa, where a is the radius of the orbit. The arclength between points A and B is αa and the distance along a straight line between A and B is 2l. From the triangle formed by A, B and the centre of the star, sin α 2 = l a (1.11) thus Tdur α P =P = sin 1 2π π l P = sin 1 a π! p (R + RP )2 b2 a (1.12) an expression of the full transit duration. The Effects of Limb Darkening: The effect caused by the stellar disk being brighter in the centre compared to the limb of the disk is called limb darkening. Photons emitted from the limb of the stellar disc at a certain atmospheric depth L, follow a more oblique path through

60 Introduction Rp/R Phase (days) Figure 1.13: Two model light curves of the super-earth GJ 1214b for observations at 5000 Å (blue) and 1 µm (orange) using a tunable filter with a width of 12 Å. Observations at shorter wavelengths result in a deeper and narrower transit. the stellar atmosphere compared to the photons emitted from the centre of the stellar disc as seen in Fig For the photons escaping the edge of the stellar disc, an optical depth of unity is reached at a higher altitude where the temperature is cooler (T LO ) and the radiation is less intense causing the apparent darkening. The limb darkening effect is largest at short wavelengths where a highly rounded light curve is observed. For longer wavelengths the effect is less severe and the centre of the transit takes on a flatter shape (see Fig. 1.13). Orbital Inclination: Radial velocity observations provide information about the minimum mass, of M p sin i, assuming the stellar mass is known. To constrain the actual mass of an exoplanet, the orbital inclination, i, has to be measured. This is done by fitting a analytical transit light curve to the data using the transit equation of Mandel & Agol (2002). A transiting exoplanet which has an impact parameter b 0 or i < 90, will have a shorter transit duration, a shallower transit depth and longer ingress and egress times. This is seen in Fig where the effects of varying i from 90 to 80 is shown.

61 Introduction Rp/R Phase (days) Figure 1.14: Inclination values ranging from 90 to 80 at 1 intervals, with the shallowest light curve corresponding to i = 80.

62 Introduction Exoplanet formation and evolution The way exoplanets form and evolve has a direct impact on the composition and dynamics of their atmospheres. The local conditions at their birth, the accretion mechanism and how they interact with their parent star, disk and potentially other planets, govern the diversity of compositions and atmospheric dynamics seen in exoplanet atmospheres today. Before the discovery of exoplanets in the 1990 s, our own solar system was the only planetary system able to provide us with observables allowing us to test theories of planetary formation. With space missions exploring the solar system throughout the latter part of the 20 th century, an enormous amount of geophysical data describing the chemical composition and internal structure of the giant planets was obtained giving clues to the origin of the solar system. With the subsequent discovery of many new planetary systems, most notably by the Kepler satellite (Borucki et al. 2010), the knowledge of planet formation was complimented by statistical properties of planetary systems with which to test hypotheses, weakening the anthropic bias (Carter 1974) of our planetary system being the only one. The birthplace of exoplanets is within the predominantly gaseous disk which surrounds protostars. The way they form however, can be divided into two formation mechanisms which all giant planet formation models rely on: disk instability model which best explains giant planets with a large mass on wide orbits, and the core accretion model, which has emerged as the dominant formation mechanism. Each of these mechanisms are described in more detail below Formation via disk instability The disk instability model (Boss 1997; Cameron 1978; Kuiper 1951) entails the formation of planets from the breakup of a protoplanetary disk due to gravitational instability forming self gravitating clumps of gas, which eventually evolve into planets. The thermodynamic state of the disk is a critical part of the model. For a disk to form, self-gravity has to dominate the thermal pressure and sheer inside the disk. The threshold for axisymmetric density perturbations to occur in a thin gaseous disk is given by the Toomre criterion (Safronov 1960; Toomre 1964),

63 Introduction 37 Q = c sκ πgσ g (1.13) where c s is the speed of sound, κ the epicyclic frequency and σ g the gas surface density. Disk fragmentation will only occur if Q 1. As such, disks with a large mass (high gravity) at low temperatures (c s = kt/m P/ρ) and high densities (σ g ) are more likely to form gravitational instabilities. Disk instability is however not enough for planets to form as a result of the fragmentation. The disk must also be able to cool efficiently on a timescale comparable to the local disk orbital period 8. Disk fragmentation is expected to more readily occur further out in the protoplanetary disk (several tens of AU) where the radiative cooling rates are higher and Q lower (Cai et al. 2006; Rafikov 2007). As such, one would expect a large number of planets on wide orbits if disk instability is the dominant formation mechanism. Janson et al. (2012) found that < 10% of FGKM-type stars form and retain companions through disk instability at 99% confidence, independent of outer disk radii (within the regime AU) taking disk migration into account. Only companions with masses < 100 M Jup were considered. Despite this result, some observations are best explained by formation via disk instability. Examples are the four giant planets (or BDs using the formation based definition of BDs) around HR 9799 with semi-major axis of 14.5, 24, 38, 64 AU (Marois et al. 2008, 2010) and Fomalhaut b (Kalas et al. 2008) at 119 AU. Although core accretion is the dominant planet formation model, the disk instability model is still a viable formation theory for gas giants with a large mass on wide orbits (Boley 2009; Dodson-Robinson et al. 2009) Core accretion model The core accretion model (Lissauer 1993; Pollack et al. 1996; Safronov 1972) is a multi-step formation process which starts with the formation of a heavy element core which forms when small solid dust grains and ices ( µm) sediment and coagulate through collisions into larger particles. These particles ( cm in size) proceed to stick together until eventually objects km in size form, known as planitesimals. Beyond this size, gravity becomes important in the development 8 τ cool /τ rot < f frag where τ cool and τ rot are the cooling and rotation time scales of the disc and f frag the ratio between them.

64 Introduction 38 of pairwise planetesimal accretion forming planetary embryos. The embryos eventually form into a planetary cores or protoplanets. When the thermal speed of the surrounding gas drops below the escape velocity of the newly formed core, gas starts to accrete around the core. Thermal pressure dictates the ever increasing growth rate which defines the runaway gas accretion phase (D Angelo et al. 2011). This continues until the reservoir of gas within the gravitational reach of the planet is exhausted. The core accretion model has in recent years emerged as the dominant formation mechanism with a large body of observations supporting it. One such observation is the steep increase in the giant planet occurrence rate as a function of host star metallicity above solar metallicity (Fischer & Valenti 2005; Santos et al. 2004). The terrestrial planets of the solar system together with the supersolar compositions and likely high mass cores of Jupiter and Saturn (Atreya et al. 2003; Guillot 2005; Militzer et al. 2008) are further examples in favour of the core accretion model. Uranus and Neptune also have envelopes enriched in heavy elements, however pose more of a challenge with their predicted formation timescales exceeding classical calculations of the lifetime of the solar nebula (Safronov 1969). More recent studies have found that this timescale can be lowered significantly under certain assumptions such as a modest enhancement of the initial surface density and if the growth takes place preferentially during the runaway planetesimal accretion phase (Pollack et al. 1996). These results are echoed by Helled & Bodenheimer (2014) who highlight the fact that different conditions in the protoplanetary disk, as well as the birth environments of the planetary embryos, can lead to the formation of planets with vastly different masses and compositions. This would provide a natural explanation for the large diversity of intermediate mass exoplanets currently observed Planet-disk interaction and migration Armed with planet formation models derived from our solar system, it came as a great surprise to find so many gas giants orbiting very close (< 0.1 AU) to their host stars in the late 90 s. This discovery is naturally biassed by observational techniques such as the radial velocity and transit techniques which are most sensitive to detecting giant planets on close orbits. A study by Howard et al. (2012) looked at 1235 planets from the Kepler mission (Borucki et al. 2010) and found

65 Introduction 39 that the occurrence rate for hot Jupiters (P < 10 days, R p = 8 32 R E ) around GK type stars is only ± For super-earths and hot-neptunes the frequency rises exponentially to the order of a few percent. Despite the lack of planets with a large mass and small semi major axis, the presence of these exoplanets sparked a widespread interest in orbital migration theory. Orbital migration occurs as a result of the gravitational and viscous interaction between the planet and the protoplanetary disk. The sheer presence of a planet in the protoplanetary disk leads to a non uniform distribution of gas within the disk. This causes torques to emerge. These torques directly influence the planets orbits during their formation periods and later the inclination and eccentricity of their orbits. The migration can occur in both directions, with local disk properties such as surface density and temperature gradients governing whether inward or outward disk migration occurs. Planets which form early on are the most likely to eventually either be ejected or consumed by the host star, while planets which form later experience a higher likelihood of developing stable orbits (Chambers 2009). The way migration proceeds also depends on the disk parameters and the mass of the planet with terrestrial planets having different formation scenarios from the EGPs (extrasolar giant planets). In the case of a low mass planet (terrestrial planet), spiral density waves form in the disk driven by the planet. The density waves which emerge introduce differences in torque between the outer and inner disk, which cause a transfer of angular momentum from the planet to the disk, leading to inward migration. For EGPs (with masses similar to Jupiter and above) a gap forms in the protoplanetary disk as a result of strong tidal interactions which acts as a tidal barrier causing the EGP to lock into the angular momentum process of the disk and prevents the flow of gas, halting accretion (Lin & Papaloizou 1986; Ward 1997). The orbital evolution of the planet gets tied to the disk causing the planet to migrate inwards on the viscous timescale of the disk. For masses in between terrestrial planets and Jupiter mass planets, such as Saturn mass planets, a partial gap in the disk might form. In such cases it is though that gas in the gap could cause torques proportional to the migration speed which could lead to both outward and inward migration (Masset & Papaloizou 2003). Migration theory is successful in explaining the orbital distribution of exoplanets and is compatible with the observed distribution exoplanet semi-major axis. A lot of work still remains to be done, especially within the migration of low-mass

66 Introduction 40 planets where there is still a great deal of uncertainty regarding the direction and rate of migration (Chambers 2009) Inflated radii of extrasolar giant planets Accurate radii measurements are required to calculate the average density and surface gravity, which determine atmospheric and internal composition as well as the dynamics, structure and evolution of exoplanet atmospheres. With such a fundamental impact on the important properties of exoplanets, understanding the diversity of measured radii is vital. A large number of transiting EGPs exhibit radii larger than predicted by models of gaseous planets with a solar composition. This inflated radius can not be explained by thermal irradiation effects from the host star alone, as a deep deposition of heat is required. This has lead to the emergence of several mechanisms aimed at explaining the inflation. Following the classification of Weiss et al. (2013) the mechanisms can be placed into three categories: tidal mechanisms, incident fluxdriven mechanisms, and delayed contraction. Tidal mechanisms: Work by Bodenheimer et al. (2001) showed that planets with an eccentric orbit or non synchronous rotation could be significantly heated through internal tidal dissipation, causing the planet to inflate until thermal equilibrium is reached. The tidal heating caused by circularisation of an initially eccentric orbit is a transient process expected to occur on time scales much shorter than the lifetime of the host star. For the eccentricity to be maintained requires the presence of a planetary companion at a few AU, capable of pumping the eccentricity. Many of the transiting exoplanets discovered to date, have small measured eccentricities consistent with a circular orbit, but still have an inflated radii. This suggests that, although tidal dissipation can be a source of internal heating, the process alone can not explain the inflated radii (Leconte et al. 2010). Incident flux-driven mechanisms: Atmospheric circulation models by Showman & Guillot (2002) demonstrated that the kinetic energy of the planets atmosphere, held in strong winds at the surface, if transported into the interior could explain the inflated radii. The winds emerge as a consequence of the strong temperature contrast between the dayside and

67 Introduction 41 nightside of the planet, a result of a tidally locked planet orbiting close to the host star. Their simulations showed that 1% of the incident stellar flux if deposited into deeper layers, could slow down the planet evolution and provide a solution to the inflated radius anomaly. Magnetic field generation in planets on close-in orbits can result in Ohmic dissipation, thought to keep some hot-jupiters inflated (Batygin & Stevenson 2010). The high level of stellar irradiation from the host-star results in a small but nonnegligible fraction of free electrons released by species with a low ionisation potential (such as atomic Na and K). These weakly ionized strong zonal winds carry the free electrons which advect across the magnetic dipole field of the planets causing an induced current which flows inwards described by Lenz law. The heat generated can either be released in the radiative part of the atmosphere, which can act as insulation for the heat present in the interior, or directly heat the interior convective zone of the planet itself (Huang & Cumming 2012; Spiegel & Burrows 2013). Work by Rauscher & Menou (2013) showed that deep Ohmic heating could successfully inflate the radius of HD b providing the magnetic field strengths occupied the 3 30 G regime, however, magnetohydrodynamic simulation studies of the atmosphere of the same planet conducted by Rogers & Showman (2014) found that the Ohmic dissipation rates can not account for the inflated radius of this planet. The difference in results emerges due to how the magnetic field geometry and evolution is treated suggesting that a self-consistent magnetohydrodynamic treatment is needed. As such, although there is no disagreement that Ohmic dissipation likely has an effect on hot-jupiter atmospheres (it is active in Jupiter and Saturn, e.g., Liu et al. 2008), the debate whether or not it can explain the inflated radii is ongoing. A large step in the right direction from an observers viewpoint would be to observe and constrain the magnetic field of an exoplanet, a task which remains to be done. Delayed contraction: A theory which does not necessarily rely on the need for an internal energy source, is that of an enhancement of atmospheric opacities which naturally retain the heat required to keep EGPs inflated (Burrows et al. 2007). The enhanced opacities could be a product of non-equilibrium chemistry, hazes, an enhancement in metallicity or simply be due to missing or underestimated opacities in current model atmospheres. This theory can not by itself explain the most highly inflated planets such as WASP-17b (Bento et al. 2014) and TrES-4b, where the opacities would

68 Introduction 42 have to be unreasonably large (much higher than 10 solar equivalent) (Liu et al. 2008). Another possible energy transporting mechanism is that of inefficient convection in the planets interior caused by heavy element gradients which have the effect of reducing the heat transport, thereby slowing down the radius contraction (Chabrier & Baraffe 2007). Similar to the enhancement of atmospheric opacity theory outlined above, this mechanism does not require an extra source of heating based on strong irradiation levels from the host star, and can thus operate on much wider orbits. The theory has its roots in the double-diffusive convection theory whereby two different compositional density gradients emerge as a result of different diffusion rates. These gradients separate the convective interior into multiple convection layers separated by diffusive layers which prohibit large-scale adiabatic convection and leads to a strong reduction of the rate of heat escape. The compositional gradients are thought to be the result of the formation history (supports the core accretion theory), giant impacts, or by the core of the planet eroding during its evolution. Observations of an inflated planet with either a sufficiently large semi major axis (a 0.1 AU for a solar type star) or observations of a reduced heat flux would support the theory of EGPs being influenced by double-diffusive convection. It is however uncertain at this point if the diffusive interfaces can last long enough (characteristic time-scale of planet formation: gigayears) to support the reduction in heat flux. Although none of the theories above can currently be ruled out, work by Demory & Seager (2011) suggests that whatever is causing the inflation is correlated with the incident stellar flux received by the planet. This signifies that enhanced opacities or the layered convection theories can not by themselves explain the inflated radii as no observations of cold inflated planets currently exist. From a sample of 115 Kepler giant planet candidates, Demory & Seager (2011) determined that radius inflation becomes effective above the orbit-averaged stellar irradiation level of erg s 1 cm 2. In Figure 1.15 this level is shown in a plot showing the planetary radius as a function of host star flux Compact radii of extrasolar giant planets The majority of EGPs show smaller radii than predicted by models which only take the irradiation from the host star into account. This is unsurprising as many

69 Introduction erg s 1 cm 2 0. < M 0.1 M Jup 0.1 < M 1.0 M Jup M > 1.0 M Jup Radius [RJup] Flux [erg s 1 cm 2 ] Figure 1.15: Planetary radii as a function of incident flux with the different mass regimes noted in the figure legend. A rise in planetary radius is observed for planets which receive an incident flux above erg s 1 cm 2. Data is from exoplanets.org. plausible scenarios would result in smaller radii, such as dense cores of rock and ice (in favour of the core accretion theory) and/or metal rich envelopes (Burrows et al. 2007). An example of an EGP which could be explained by a denser core or metal rich envelope is HD b, which has a substantially smaller radius than expected, R = (0.725 ± 0.05)R J compared to R = 1.14 R J for a planet of equal mass but pure solar composition (Sato et al. 2005). Not all objects can be explained by this theory however, as is the case with CoRoT-20b which has one of the highest densities discovered to date (8.87 ± 1.10 g cm 3 ) (Deleuil et al. 2012), challenging planet formation and interior structure modelling. Such a high density (Earth average density is 5.52 g cm 3 ) would require an enormous amount of heavy elements, approximately > 700 M Earth of heavy materials in the central core (see Fig. 1.16) which compared to current planet formation models (Alibert et al. 2005; Mordasini et al. 2009) would require an extraordinary high efficiency in processing heavy material from the disk to the planet. An alternative theory which would require a smaller amount of heavy material is if the heavy elements are more evenly distributed throughout the planets interior and not just in the central core (red solid line in Fig. 1.16). Although this would reduce the requirement for enrichment, it would imply a disk-to-planet processing efficiency of 60% which is roughly twice of what current planet formation models predict. A simple solution

70 Introduction 44 H/He CoRoT-20b Figure 1.16: Radius evolution tracks of a 4 M Jup object, representative of CoRoT-20b. The black dotted line corresponds to a pure H/He planet. The magenta dashed curve is a model for a planet with a 850 M Earth central core and the red solid line is a model with about 500 M Earth of heavy material evenly distributed across interior of the planet (models created by I. Baraffe following Baraffe et al. 2008). Figure used with permission from I. Baraffe. to the problem would be if the radius of CoRoT-20b was underestimated due to an incorrect determination of the host star radius caused by the presence of an unresolved binary companion to the exoplanet host star or by a line of sight blend with another star. In this case the combined flux from both stars will be measured, causing the radius ratio of the exoplanet (which relies on a correct determination of the stellar radius) to be underestimated. At a distance of 1.23 ± kpc and with a magnitude of V mag, CoRoT-20b becomes a challenging object for direct imaging follow up, suggesting that the radial velocity holds the most promise of finding a companion. WASP-12b, a very inflated hot Jupiter is a good example of how an incorrect radius determination can occur as a result of an unresolved companion. At a

71 Introduction 45 projected distance of roughly 1 away from WASP-12, a close by M-type companion candidate 9 called Bergfors-6 (Bergfors et al. 2013), went unnoticed. Not accounting for the companion candidate caused an underestimation of the transit depth in previous studies. Correcting for this made WASP-12 hotter and larger which also had a knock on effect on the inferences of its atmospheric composition (see Crossfield et al. 2012; Sing et al and references therein) Characterising Exoplanet Atmospheres Once the mass and radius of an exoplanet has been inferred from indirect observations of the exoplanet host star, the average density of the exoplanet can be calculated. This, together with chemical and physical properties of the planet, can give us important information about the bulk composition. To obtain information beyond bulk composition and to lift possible degeneracies, requires information about the atmospheric composition and structure. Observations of an exoplanet atmosphere might help lift the degeneracy between an extended atmosphere covered by clouds and hazes or a compact atmosphere composed of heavier elements, both of which have similar average densities. Transiting planets provide excellent opportunities for atmospheric studies as their atmospheres can be studied during primary eclipse (transmission spectroscopy), during secondary eclipse (emission spectroscopy) and in between the two extrema (phase curve observations). The atmospheres of an exoplanet can also be studied by obtaining spectra from directly imaged planets (e.g., Barman et al. 2011) or by observing the phase curve of a planet which does not transit (e.g., Lockwood et al. 2014) Transmission Spectroscopy Transmission spectroscopy is a technique used to gather details about the chemical composition and vertical extent of a planets atmosphere. The opacity of an exoplanet atmosphere decreases as density decreases with altitude. As light from the host star passes through this atmospheric shell, a small portion of the starlight is absorbed. The amount of starlight absorbed is wavelength-dependant due to the scattering properties of the atoms and molecules in the exoplanet atmosphere. The 9 (Bergfors et al. 2013) note that Bergfors-6 has been observed to have an elongated shape at two different epochs, suggesting the companion candidate might itself be a binary.

72 Introduction % ~0.02% Figure 1.17: A transit light curve schematically showing the light blocked out by the opaque disk of the planet (black line) and the light blocked by the semi-transparent atmosphere. A typical hot-jupiter transit depth is 1 2% wheras the transit depth caused by the atmosphere is 0.02%. presence of a strong atomic or molecular transition will make the exoplanet atmosphere more opaque. This effectively increases the radius of the planet. Observing the different transit depths (caused by the different radii) at specific wavelengths, allows the presence of specific light absorbing atoms and molecules to be inferred. This difference in depth of the light curve as a function of wavelength allows for the creation of a transmission spectrum which can be used to derive the chemical composition and physical properties of an exoplanet atmosphere. The transit depth is usually expressed as a radius ratio between the planetary and stellar radius, which is measured during transit, instead of the absolute radius of the planet. This allows the planetary radius to be updated as the stellar radius becomes better constrained through observations. To detect a certain atmospheric constituent, and to possibly estimate the abundance, the radius of the planet is measured at multiple wavelengths during a transit event. This is done either using filters with a specific band pass, or using a spectrograph. At certain specific wavelengths, the atmospheric species of molecules and atoms at high altitudes will make the exoplanet atmosphere more opaque. The expected variation in transit depth are on the order of a hundredth of a percent, requiring high signal to noise measurements (Fig. 1.17). It is therefore essential that as many photons as possible are collected to increase the signal to noise ratio.

73 Introduction HD b HD b HD b 9 Vmag HAT-P-1b GJ 1214b Atmospheric signal required to detect a 1 atmospheric scale height feature [%] Figure 1.18: V mag as a function of the atmospheric signal required to detect an atmospheric features 1 scale height in size. The curved lines represent lines of constant S/N. The top red dotted line indicates the required S/N for mmag photometry (S/N 1087), whilst the solid blue line below represents a S/N 2000 which is typically achieved with a single HST orbit (based on data from Nikolov et al. 2014). The three bottom curves in green represent the S/N which would be achieved with 5, 10 and 20 times the incident photons compared to the solid blue line. Favourable targets for atmospheric studies orbit bright stars and have an extended atmosphere making the atmosphere easier to detect (direction towards the top right of the plot). The hot-jupiter HAT-P-1b (blue) and the super-earth GJ 1214b (green), which are discussed in more detail later in 4.1 and 4.3 respectively are shown for comparison. Data from exoplanets.org.

74 Introduction 48 Transit observations intended to detect atmospheric constituents are usually carried out using either large ground based telescopes, or space telescopes which are not affected by the turbulence in Earths atmosphere. An exoplanet atmosphere will be easier to characterise if the host star is bright, if the radius ratio between the planet and star is large and if the atmosphere has a large scale height. The super-earth GJ 1214b, despite having a small radius compared to hot-jupiters, has been a favourable target to study as it orbits a M-type star which has a smaller radius leading to a more favourable radius ratio. Fig shows the brightness of the exoplanet host star (providing high S/N measurements), as a function of atmospheric signal The Transmission Spectrum Transmission spectroscopy observations are commonly compared to detailed atmosphere models which incorporate variations in temperature, pressure, and composition as a function of altitude which the data can in principle constrain. The propagation of photons through these models are calculated using radiative transfer equations, which are solved using numerical integration allowing theoretical transmission spectra to be produced. However, by interpreting observations with an analytical model, which includes the relevant physics, valuable insight can be gained into the physical phenomena which impact the transmission spectrum. An extended exoplanet atmosphere with a large atmospheric scale height H, is easier to detect and characterise compared to an atmosphere with a small H, as more light is obscured by the atmosphere at a given wavelength. The atmospheric scale height, which describes the distance over which the pressure decreases by a factor e is defined as: H = kt µ m g (1.14) where k is Boltzmann s constant, T is the atmospheric temperature, µ m is the mean molecular weight, and g the local gravitational acceleration. The optical depth τ of the planet s atmosphere is dependent on the atomic and molecular opacity of the gas and the structure and composition of the clouds. τ can be expressed as function of wavelength λ and altitude z as,

75 Introduction 49 τ(λ, z) σ abs (λ)n(z) 2πR p H (1.15) following the procedures of Fortney (2005), where σ abs is the cross section of the main absorbing species, n(z) the volume density at height z, and R p the radius of the planet. The number density can be assumed to vary with height exponentially (n(z) = n 0 e z/h ) in accordance with the barometric formula. Lecavelier Des Etangs et al. (2008) showed that as the light passes through the exoplanet atmosphere at slant angles, the optical depth remains approximately constant at τ 0.56, providing R p /H is between 30 and The effective radius of an exoplanet can thus be approximated by an optical thickness of τ eq defined as τ eq = 0.56 τ. Under the assumption of an isothermal atmosphere in hydrostatic equilibrium, and assuming H R p and that the abundance or mean molecular weight does not change with height, the effective altitude of the transmission, z, can be expressed as a function of wavelength following the procedures of Lecavelier Des Etangs et al. (2008): ( ) z(λ) = H ln ξ abs P z=0 σ abs (λ)/τ eq 2πR p /kt µg, (1.16) where ξ abs and σ abs are the abundance and cross section of the dominant absorbing species respectively, P z=0 the pressure at the reference altitude and R p the radius of the planet. To illustrate which parameters affect the transmission spectrum and to what extent, the ratio R of the altitude difference between two model transmission spectra is derived. The change in altitude is expressed as the difference between the central line core z(λ core ) and the line wing z(λ wing ) of a potassium line. Mathematically the ratio R is expressed as, R = z(λ core) z(λ wing ) II z(λ core ) z(λ wing ) I, (1.17) where the subscript I represents the first model, and II the second. Substituting Eq into Eq the ratio becomes,

76 Introduction K 1500 K 1000 K Rp/R Wavelength [Å] Figure 1.19: Potassium line profile showing the effects of temperature. As the model temperature increases from 1000 K (blue) to 1500 K (orange) and finally to 2000 K (red), the line cores increase in strength whilst the line wings steepen. R = { kt ln µg { kt ln µg ( ξ core σ core µwing T wing ξ wing σ wing µ core ( ξ core σ core µwing T wing ξ wing σ wing µ core T core ) 1/2 } II T core ) 1/2 } I. (1.18) ξ Following the assumptions stated above, core µ ξ wing, wing µ core and T wing T core are all equal to one as they do not change with altitude. However, by evaluating the terms in equation 1.18 individually (done in the next subsections), the effects of changing the temperature, abundance or mean molecular weight, on the altitude difference R, can be assessed The effects of temperature on R Considering the effect a temperature change has on the potassium line profile keeping all other parameters fixed, R can be expressed as,

77 Introduction ξ K 10 ξ K 1 ξ K Rp/R Wavelength [Å] Figure 1.20: Potassium line profile showing the effects of abundance. As the model abundance of potassium increases from 1 (blue) to 10 (turquoise) and finally to 100 (green) solar abundance, the entire profile shifts upwards, retaining it s shape. R = T II T I (1.19) where T I and T II represent the temperatures of model I and model II respectively. For the altitude difference between the line core and the continuum to double in size would require the temperature to double. The effects of changing the model temperature can be seen in Fig where the parameters of HAT-P-1 b were used. In addition to the amplitude of the spectrum increasing, an increase in temperature causes an increase in the thermal motion of the potassium atoms causing an enhanced Doppler broadening seen as an increase in opacity in the line core and steeper line wings, a result of a wider Gaussian velocity distribution The effects of changes in abundance on R Considering the effect an abundance change has on the potassium line profile keeping all other parameters fixed, R becomes equal to one as ξcore ξ wing = 1. As such

78 Introduction m u 2.35 m u 5 m u Rp/R Wavelength [Å] Figure 1.21: Potassium line profile showing the effects of changing the m u of the model with m u = 1 (blue), m u = 2.35 (pink) and m u = 5 (purple). Since Eq assumes a constant m u, the various models do not show the affect of m u changing as a function of altitude, but rather various models using a constant m u throughout. A decrease in m u results in a steeper profile with the line cores increasing in strength. An increase in m u results in a decrease in a flattening of the line wings and a line core which diminishes in strength. the potassium profile does not increase in size. Instead the increase in abundance causes a uniform increase in opacity at all wavelengths and as a result the entire profile shifts upwards retaining it s shape as shown in Fig The effects of mean molecular weight on R As the scale height of an exoplanet atmosphere is inversely proportional to the mean molecular weight (µ), only a decrease in molecular weight would cause an increase in the altitude difference. There is however a limit to how low µ can become limited by the fact that hydrogen can not be divided further, requiring the mean molecular weight to be µ m u, where m u is the atomic mass unit. A typical value for µ is taken to be 2.35 m u due to the composition of gas giant exoplanet atmospheres being predominantly composed of H 2 (2 m u ) and He (4 m u ) together with molecules of higher molecular weight. For observations which probe

79 Introduction 53 the upper most atmosphere, where the fraction of ionized atoms are greater, such as with UV observations, a value of µ = 1.2 m u is used instead (Bourrier et al. 2014). Considering the effect a change in mean molecular weight has on the potassium line profile keeping all other parameters fixed, R can be expressed as, R = µ II µ I (1.20) The effects of changing the mean molecular weight can be seen in Fig An increase in the mean molecular weight causes a flattening of the potassium profile with widening line wings. This is caused by an increase in pressure with the line cores diminishing in strength as the scale height (H = kt/µ m g) decreases.

80 Introduction The Impacts of Stellar activity Stellar activity can have a profound impact on exoplanet transit measurements. The presence of star spots during a transit can easily complicate the interpretation of the transit data introducing the need for activity corrections, as the transit depth is directly influenced by the presence of star spots. It will be underestimated in the event where the planet transit crosses a star spot, and overestimated with the presence of unocculted star spots on the stellar surface. A wavelength dependence is also introduced, as the stellar flux lost by the spots, at a given wavelength, will depend on the blackbody temperature difference between the stellar surface and the spots (Czesla et al. 2009). The stellar spots also create a quasi-periodic photometric variability, as the spots rotate into and out of view with the stellar rotation period, changing their shape as they evolve. Activity corrections are also crucial for phase curve observations. For these events the modulations in flux due to the star must be carefully subtracted from that of the exoplanet in order to accurately interpret the phase curve. To determine the level of flux contribution of the star and to what degree this influences the amplitude of the exoplanet phase curve, the magnitude of the stellar variability needs to be accurately measured. An example of how photometric variability monitoring of exoplanet host stars aid in the accurate determination of transit depths and phase curves is presented in the work by Huitson et al. (2013, 2014) and Nikolov et al. (2014) who used observations taken at the 1.3 m CTIO (Cerro Tololo Inter-American Observatory) telescope during the 2012AB (PI: Wilson, P. A.) and 2014A (PI: Wilson, P. A.) semester Thermal inversions Stellar irradiation is one of the most important factors in determining the atmospheric properties of exoplanets as it has direct impact on the structure, chemistry and temperature of the exoplanet atmosphere. Furthermore, stellar irradiation is directly linked with atmospheric escape, for example the evaporation of the upper atmosphere of HD b has been shown to be caused by X-ray/EUV-radiation being deposited (Lecavelier Des Etangs et al. 2008) in the upper atmosphere. Highly irradiated exoplanets are predicted to have thermal inversions as a result of a high altitude opacity source absorbing the incoming stellar irradiation in

81 Introduction TiO/VO Rp/R no TiO/VO Wavelength [Å] Figure 1.22: The difference in transmission spectra with TiO/VO (upper orange) and without (lower blue) for a 1500 K isothermal, hydrostatic and uniform abundance model (Fortney et al. 2008, 2010). The TiO/VO model has been vertically offset for clarity. the UV/optical. Thermal inversions of this sort are not uncommon in the solar system planets. Earth and Jupiter are excellent examples with temperature inversions caused by the absorption of UV flux by ozone (O 3 ) and by hazes caused by methane photochemistry respectively. Amongst the hottest hot Jupiters, there are a number of observations, which when interpreted using model atmospheres, have shown to be consistent with a thermal inversion such as HD b (Burrows et al. 2007; Knutson et al. 2008), HD b (Harrington et al. 2007), XO-1b (Machalek et al. 2008) and CoRoT-1b (Deming et al. 2011). It has been suggested that this could be due to the presence of TiO and VO (Burrows et al. 2007; Fortney et al. 2008; Hubeny et al. 2003) or due to photochemical hazes (Zahnle et al. 2009) (products of photochemistry or other non-equilibrium processes, see 1.3.7) with high optical opacity. The absorption at high altitudes, leading to a thermal inversion also makes the exoplanets appear brighter in secondary eclipse measurements at mid-infrared wavelengths, with molecular bands such as water seen in emission rather than absorption. A classification scheme which divided exoplanets with dramatically different spectra (see Fig. 1.22) and day/night contrast due to TiO/VO was suggested by Fortney et al. (2008). In this scheme the hotter pm class of exoplanets are hot enough to have their opacity dominated by TiO and VO absorbing in the optical. The

82 Introduction 56 pl class on the other hand, with temperatures below the condensation curve of Ti and V bearing compounds, will have their spectra dominated by the alkali metals in the optical, and H 2 O and CO in the near-ir with shallow secondary eclipse depths and a small day/night contrast being the hallmark of this type of planet. Observations have not yet shown a clear cut-off between the pm and pl types. WASP-14b and TrES-3b which are highly irradiated planets do not have a temperature inversion, suggesting that either stellar or planetary characteristics other than temperature affects the presence of inversions (Blecic et al. 2013; Fressin et al. 2010). An example of such a characteristic is the proposed correlation between stellar activity and thermal inversions (Knutson et al. 2010), whereby an active star with a high UV flux may destroy any compounds which would otherwise cause an inversion. The carbon-to-oxygen (C/O) ratio has a direct influence on the relative concentrations of several species, such as H 2 O and CO 2, which greatly affect the emergent spectra. A C/O 1 causes a natural underabundance of TiO/VO which can prevent a thermal inversion from occurring. As such, Madhusudhan (2012) suggested a classification scheme based on both a C/O ratio and stellar temperature / irradiation. More observations are needed to conclusively constrain the C/O ratios of exoplanetary atmospheres, although several planets observed thus far are consistent with C-rich atmospheres. The lack of inversion seen in some of the highly radiated planets like WASP-19b (Huitson et al. 2013) and WASP-12b (Sing et al. 2013), could be due to the depletion of TiO/VO either through gravitational settling (Spiegel et al. 2009) or by TiO/VO raining out of the atmospheres at colder temperatures. In the first scenario macroscopic mixing such as turbulent diffusion or large scale convective motions is essential for TiO/VO to stay aloft in the atmosphere as TiO/VO which are significantly heavier molecules compared to molecular hydrogen, would otherwise sink and settle deeper in the atmosphere. In the second scenario, TiO/VO could rain out of the atmosphere at lower temperatures and higher pressures as TiO/VO condense into solid grains and sink. This could happen in a cooler region of the atmosphere below the inversion known as the cold trap. Hot Jupiters are thought to be tidally locked which causes large temperature differences which introduces strong winds which flow from the hot day side to the cool night side at speeds on the order of a few km/s (Snellen et al. 2010). Such strong winds could transport the gaseous TiO/VO to the cooler night side where it condenses

83 Introduction 57 out causing a significant TiO/VO depletion on timescales of a few hundred millions of years in the upper dayside atmosphere (Spiegel et al. 2009). There has been no clear detection of TiO/VO through means of transmission spectroscopy to date. This statement follows a caveat that since transmission spectroscopy is only sensitive to the atmosphere at the terminator of a planet, it could still exist in the hotter upper atmosphere of the dayside of the planet Clouds and Hazes in Exoplanet Atmospheres Clouds are generally regarded as a mass of liquid or solid particles which form when the vapour pressure of the particles exceeds their saturation vapour pressure. Hazes on the other hand are generally considered as products of photochemistry or other non-equilibrium processes (Marley et al. 2013). Aerosols is the all encompassing term which includes particles of any size and kind which are suspended in the atmosphere, although it is commonly used to describe very small particles which do not precipitate out of the atmosphere (Seager 2010). Clouds and hazes play an essential role in the atmospheric energy balance of substellar objects and are closely linked with atmospheric dynamics. Their opacities affect the emergent flux and atmospheric temperature-pressure profiles which directly influences observations. For example, their obscuration of emergent spectral features alter the resulting transmission spectra and their reflective properties, which changes the geometric albedo, impacting phase curve observations. The impact of clouds and hazes is evident in roughly half of the exoplanet atmospheres discovered to date (D. K. Sing. priv. comm.) 10. Clouds and/or Hazes have been observed in hot-jupiters such as HD b (Pont et al. 2008), WASP-12b (Sing et al. 2013), HAT-P-32b (Gibson et al. 2013) and WASP-6b (Jordán et al. 2013). Clouds have also been found to be present in the super-earth GJ 1214b, where a featureless transmission spectrum has been observed across a wide range of wavelengths from the optical to the near-ir, due to the presence of clouds (Kreidberg et al. 2014). Clouds are also likely present in the atmosphere of HD 97658b, a super-earth with a transmission spectrum best described by an obscuring cloud deck or a metal-rich atmosphere (Knutson et al. 2014). There are a number of different cloud models which differ significantly in their approach. Despite the different approaches, most of the cloud models have many 10 Based on preliminary results from a large HST program, GO-12473

84 Introduction 58 similarities. Cloud models all need to assume a gas composition which in most cases is assumed solar or super-solar (enhanced abundances). The temperaturepressure (T-P) profile, which governs when the constituents of the atmosphere condense out is derived from radiative - convective equilibrium calculations which are dependent on lower boundary conditions from interior models (e.g., Baraffe et al. 1998). Beyond the above description, cloud models start to diverge in their approach. Some of the main cloud models are summarised in the next section Cloud models Ackerman & Marley (2001) presented a method of calculating vertical profiles of particle size distributions in condensation clouds of giant planets and BDs. The method assumes a balance between a downward transport of particles by sedimentation and the upward turbulent mixing of condensate and vapour. Assuming a uniform cloud deck (globally averaged) the balance is presented as: K zz q t z f sedw q c = 0 (1.21) where K zz is the vertical eddy diffusion coefficient, q t the mixing ratio of condensate and vapour (q t = q c +q v ), q c the mixing ratio of the condensate, w is the convective velocity scale, and f sed, a dimensionless parameter describing the efficiency of the sedimentation. A high sedimentation efficiency produces clouds with large particles which settle into vertically thin layers. A low sedimentation efficiency on the other hand, produces vertically extended clouds composed of smaller particles, making them optically thicker (Morley et al. 2012; Stephens et al. 2009). method does not rely on the treatment of microphysical processes to compute particle sizes and the formation of clouds in BD and planetary atmospheres. This makes the solution numerically rapid, allowing a large number of models to be generated within a relatively short time frame (Marley et al. 2013). The solution of the equation provides the total amount of condensate and particle sizes for each layer in the atmosphere above an arbitrary cloud base. In the previous model, vapour and condensate is dredged up from deeper in the atmosphere before being transported downwards by sedimentation. The Models by Helling & Woitke (2006) have taken a different approach by modelling the complex process of condensate grain formation which starts off with seed particles a the

85 Introduction 59 top of the atmosphere. The nucleation process itself is computed as the seeds fall reacting with the gas and accreting condensate material. The top-down approach adopted by Helling and collaborators compared to the bottom-up approach by models akin to Ackerman & Marley causes a difference in predicted composition. Although a number of cloud models have been compared (Helling et al. 2008) to each other, the complexity of the Helling et al. models has made the computational approach challenging, and limited comparison between models and observations (Marley et al. 2013). As such, which model best matches observations for range of conditions, remains to be fully determined.

86

87 Chapter 2 Observations & Data Reduction 2.1 Observations in the optical The night sky in the optical Compared to the near-ir night sky, the optical night sky is relatively free of emission lines towards bluer wavelengths with the strong neutral oxygen lines (see Fig. 2.1) being the exception. Moon light does affect the sky background (dependant on phase) by reflecting sunlight onto molecules in the atmosphere thereby increasing the sky background. Even in the absence of the Moon, Zodiacal light which is sunlight reflected off dust grains located in the inner solar system can also increase the brightness off the sky background. Zodiacal light predominantly affects observations during dark time with objects located towards the ecliptic and is most dominant in the V-band. The zodiacal light is one of the major contributors to the total HST sky background, together with Earthshine light and geocoronal line emission (originating from photochemical reactions involving hydrogen and oxygen atoms in the Earth s exosphere) (Giavalisco et al. 2002). The geocoronal line emission, also known as airglow, changes on timescales of years to minutes getting systematically fainter as the night progresses (Krisciunas 1997). Down on Earth, light pollution can be a major contributing factor on sky-background in the optical especially as many street lights use sodium-vapor lamps. Solar activity will also affect the sky brightness within all optical bandpasses. As the level 61

88 Observations & Data Reduction 62 Flux ( erg s 1 cm 2 1 arcsec 2 ) OI [5577 ] U B V R I OI [6300 ] OI [6364 ] OH Meinel bands Na I D NI [5200 ] Wavelength ( ) Figure 2.1: A wavelength and flux calibrated sky spectrum (black line) showing prominent emission lines together with broadband filter throughput curves. The night sky spectrum is taken from the FORS1 night sky spectral library (Patat 2008) where observations were done with a 1 slit using the G300V grism. The spectral resolution is λ = 12 Å. The filter throughput curves (coloured lines) are the Bessel filters from the Nordic Optical Telescope (Filters #1,2,3,4,5) and have been arbitrarily normalised. of solar activity decreases, so does the sky background in a linear fashion (Patat 2008) Reducing optical imaging data Reduction of optical imaging data in its most basic form, consists of subtracting the pixel value bias added to the images to avoid negative pixel values in the science images, before subsequently dividing the science images by a flat field. The flat field is created by imaging a uniform screen or the sky at dusk/dawn. The purpose of the flat field is to remove as much of the non-uniform ADU count variations across the detector which occur as the result of pixel to pixel sensitivity variations, time-varying dust accumulation on optical elements and alterations to the throughput such as vignetting. In the event where thermal noise is significant, dark frames should be acquired with exposure times equal to that of the observations. With instruments cooled sufficiently such as with liquid nitrogen, dark frames are not necessary as the dark current is negligible. Such is the case with the OSIRIS instrument at the GTC telescope.

89 Observations & Data Reduction Narrowband Spectrophotometry using tunable filters Narrowband spectrophotometry is a technique which bridges the gap between imaging observations and low resolution spectroscopy. Tunable filters (TFs) are a special type of narrowband filters which have the unique capability of altering the wavelength of maximum transmission and in some cases the bandpass. This is particularly useful when studying specific features such as Lyα emitter galaxies at high redshift (de Diego et al. 2013; Swinbank et al. 2012) or atmospheric absorption in the atmospheres of hot-jupiters (Colón et al. 2010; Sing et al. 2011) and super- Earths (Wilson et al. 2014). Tunable filters provide high signal-to-noise S/N at good resolutions which is necessary for studying the atmospheres of exoplanets. Altering the wavelength of the tunable filters also makes it possible to avoid major sky lines such as the O I and OH emission lines described in and shown in Fig 2.1, which might otherwise interfere with the observations The Fabry-Pérot Interferometer To allow for high S/N measurements at specific wavelengths, such as when probing a specific part of the transmission spectrum, a Fabry-Pérot interferometer can be used. In 1899 C. Fabry and A. Pérot designed the interferometer, which unlike the Michelson interferometer which splits the light into two beams, the Fabry-Pérot Interferometer splits the light into multiple beams creating a fringe pattern which is much sharper due to the interference of multiple rays of light. The setup consists of two parallel, semi-transparent, reflective plates at a fixed distance apart, known as the etalon. As the incident light enters the system it is reflected a number of times before exiting the system forming sharp fringes. These fringes are the interference pattern caused by constructive interference, a result of two or more light beams which have a path difference equal to a integer multiple of λ. Shown in Fig. 2.2 are two partially reflective surfaces a distance d apart being illuminated by light incident at an angle φ. The difference in path lengths P between the emerging beams of light is: P = 2d cos φ (2.1)

90 Observations & Data Reduction 64 Figure 2.2: The optical path of the Fabry-Pérot interferometer. with constructive interference occurring when the path is an integer multiple of the wavelength, µ P = Nλ (µ is the refractive index of air) such that λ = µ2d cos φ. (2.2) N The OSIRIS instrument at the GTC telescope uses a very narrow plate separation resulting in a wide separation between the successive interference peaks. Using a blocking filter, the order of interest is isolated allowing the system to only let through light over narrow wavelength range. Moving outward from the optical center causes a shift towards bluer wavelengths. In the case of relative photometry, the target of interest and reference star has to be placed at the same distance from the optical center to ensure observations at the same wavelength. As the light passes through the etalon it is either transmitted or reflected. To calculate the transmitted light intensity I T we need to know the complex amplitude of the electric field E since: I = cµɛ 0 2 E 2 (2.3) where c is the speed of light, µ the refractive index and ɛ 0 vacuum permittivity. Following Fig. 2.2 the transmitted electric field can be expressed as:

91 Observations & Data Reduction 65 E T = E 0 t 2 + E 0 t 2 r 2 e iδ + E 0 t 2 r 4 2e 2iδ +... (2.4) which is a geometric series whose sum is given as E T = E 0t 2 1 r 2 e iδ (2.5) Substituting Eq. 2.5 into Eq. 2.3 and expressing T = t 2, R = r 2 and = δ + δ r gives I T = I 0 T 2 1 Re iδ 2, (2.6) were the denominator can be expressed in terms of trigonometric functions as: I T = I 0 T 2 1 R F sin 2 ( /2) (2.7) where F = 4R/(1 R) 2 is the finesse of the interferometer describing the sharpness of the interference fringes. Ideal Fabry-Pérot fringe profiles with various reflectivities are shown in Fig. 2.3.

92 Observations & Data Reduction R = 0.95 R = 0.50 R = 0.25 Transmission (I/I0) Wavelength (Å) Figure 2.3: An ideal Fabry-Pérot fringe profile showing transmitted intensity as a function of wavelength for plates with 95%, 50% and 25% reflectivity and plate separation of 3µm. By adjusting the plate separation, a desired wavelength can be chosen and together with a blocking filter the contribution from the other orders can be removed. 2.2 Observations in the near-ir The near-ir sky Observations in the near-ir are challenging for a number of reasons. Compared to the optical, the near-ir sky is dominated by the vibrationally excited OH molecules which are created when hydrogen and ozone react. The highly variable OH emission contributes significantly to the sky background making it variable on time scales of tens of seconds to minutes. Beyond a wavelength of 700 nm, the OH emission lines start to dominate and continue to do so until wavelengths longward of 2.3 µm where a steep increase in flux density is observed due to thermal black body radiation from the sky and the telescope itself. This effect is amplified by the presence of thin clouds (e.g. cirrus clouds) which have the effect of reflecting heat of Earths surface. Although the OH emission lines can be a nuisance for astronomical observations, especially low resolution spectroscopy and imaging of faint objects, they can also serve as good wavelength calibrators (Osterbrock et al. 1996; Rousselot et al. 2000). At near-ir wavelengths (1 to 2.5 microns) many absorption features caused by water vapour and carbon dioxide

93 Observations & Data Reduction Js Ks Transmission J H K Wavelength (µm) Figure 2.4: The near-ir sky transmission spectrum shown together with broadband filter throughput curves. The transmission spectrum is generated by ATRAN (Lord 1992) and is hosted on the Gemini Observatory webpages. The tranmission spectrum is specifically generated for Mauna Kea assuming an airmass of 1.0 and a water vapour coloumn of 1.6 mm. The filter throughput curves (coloured lines) are the standard SofI filters at the ESO NTT telescope. exist. The near-ir transmission spectrum is shown in Fig. 2.4 whilst the emission spectrum is shown in Fig Both figures are shown with common near-ir filter profiles for reference Reducing near-ir imaging data To account for the pixel response variation of the near-ir array, flat fields are acquired to create a master flat which the science images can be divided by. Sky flats, or dome flats are taken in two groups, a set of brighter flats and a group of fainter flats all with the same exposure time. This is to allow for the thermal emission from the telescope and instrument to be subtracted. As the array experiences noise due to thermal noise, darks are taken and subsequently subtracted from the array. For the brown dwarf monitoring observations with SofI at the NTT, a set of special flats were done. This was done to remove a residual shading pattern which varies as a function of the DIT (Detector Integration Time) and the incident flux. In addition to the regular flats (bright and a dark flat), the focal plane mask was placed such that the array was partly obscured with one part evenly illuminated and the other part dark (see Fig. 2.6). The dark section can then be used to

94 Observations & Data Reduction 68 Flux ( erg s 1 cm 2 1 arcsec 2 ) Js J H Wavelength (µm) Ks K Figure 2.5: A wavelength and flux calibrated sky spectrum (black line) showing prominent emission lines together with broadband filter throughput curves. The night sky spectrum is generated by ATRAN (Lord 1992) and is hosted on the Gemini Observatory webpages 1. The sky emission data is specifically generated for Mauna Kea assuming an airmass of 1.0 and a water vapour coloumn of 1.6 mm. The filter throughput curves (coloured lines) are the standard SofI filters at the ESO NTT telescope and have been arbitrarily normalised. characterise the shading pattern. This pattern, becomes especially important when dithering or nodding in the y-direction as this is the direction the shading changes the most. In the near-ir, the sky background is orders of magnitude brighter than the optical sky, primarily due to a plethora of OH emission lines, but also due to molecular oxygen (1.27 µm) and water (end of K-band) (see 2.2.1). To be able to detect faint sources, the sky background emission has to be removed. This can be done either by using sky suppressing filters, which have shown to be capable of supressing 400 OH lines across the µm range, resulting in a background times fainter (Bland-Hawthorn et al. 2011), or by using dithering techniques. The latter technique works by taking multiple images, dithering the telescope between each exposure allowing a median combined image without stars to be created (a sky image), which then can subsequently be subtracted. Sources in the sky subtracted images will have a greater S/N allowing for measurements of higher photometric precisions to be made. For photometric time series measurements, sky subtracted images provide a better centring of the photometric aperture. The drawback of the dithering technique is that it inevitably introduces systematic errors as the objects of interest falls on different pixels, each with different responses. The flat

95 Observations & Data Reduction 69 y (pix) x (pix) ADU y (pix) Figure 2.6: A frame from the special flat sequence with focal plane mask partially obscuring the array (left) allowing the residual shading pattern to be measured. Median combining along the columns of the white box, the shading pattern is clearly seen (right). field calibration images limit this variation, but is not able to remove the variations completely, in part due to the sensitivity of the flat field varying depending on the illumination level. To limit the systematic noise, stare mode observations whereby the object of interest is kept on the same set of pixels throughout the observing sequence can be used. This is a technique commonly used with observations from space where Earth s sky background is no longer an issue, although it can also be used from the ground. The technique works best for bright objects, but is not suitable for ground observations of faint targets such as T-type brown dwarfs which have magnitudes comparable to the sky background. In such cases the centring of the aperture becomes unreliable introducing systematic effects. The best photometric technique will also depend on the seeing conditions and airmass High precision near-ir photometric monitoring of brown dwarfs Nodding Technique: For the BAM follow-up study of variable brown dwarfs a nodding technique was adopted. This technique, is based on doing only one dither step to obtain an on and off-field image allowing for the sky background to be subtracted. The technique is frequently used in other parts of astronomy such as when observing extended

96 70 Observations & Data Reduction 1000 y (pix) x (pix) Figure 2.7: A raw SofI nodding image of a crowded field created by median combining two set of images and subtracting one combined image from another. objects, where a dither pattern is not sufficient. For the brown dwarf monitoring observations the nodding technique was used stepping between two pixel locations on the array. This had the benefit of allowing the sky background to be properly subtracted whilst at the same time minimising the inter-pixel variations by having the objects of interest fall on the same two pixel locations on the array. To further minimize the systematic pixel variations which could occur in the event of poor guiding (caused by a faint guide star or bad seeing) or because of instrument flexure, which might affect the sub-pixel tracking, a slight defocus (seeing ) was used. To obtain the best possible guiding, a red guide star (most similar in colour to the BDs) was selected, when possible, to minimise guiding errors due to differential atmospheric refraction. For the technique to work efficiently, the array also needs to be checked to ensure the object of interest and some of the best reference stars do not fall on faulty pixels. The drawback of this technique is that for crowded fields, some objects will inevitably fall on the previous position of other stars in the field, causing their flux values to become unreliable. Fig. 2.7 shows a typical unprocessed nodding image.

97 Observations & Data Reduction 71 Illumination correction: As the illumination of the sky is not accurately represented by dome screen flats or sky flats, residual low frequency sensitivity variations exist in the SofI data after the sky subtraction and the division by a normalised flat has been done. To account for this low frequency sensitivity variation across the array (typically a few percent), illumination corrections were done for the BAM survey. By observing a standard star in a grid like pattern across the array, a low order polynomial can be fitted by placing a standard star of known brightness at various positions across the array in a grid pattern. This 2D surface is subsequently normalised and multiplied by the normalised flat to create an illumination corrected flat which the science data can be divided by. As both the flats and the intensity of the dome lamps change with time, a set of illumination correction observations were done every night of observing. 2.3 Sources of noise Detector noise Read noise The read noise is the noise (independent of signal level) associated with converting measured electrons to an analogue voltage and subsequently converting this to a Analogue to Digital Unit (ADU). Subtracting one bias image from another ( B) and creating a histogram of the pixel values, results in a gaussian distribution with a width characterised by the read noise and the gain of the detector: N R = G σ B 2 (2.8) which for multiple read outs (NDITs) becomes: σ RN = n pix N R (2.9) where G is the gain of the detector in units of e /ADU and n pix the number of pixels. The speed at which the detector is read out affects the read noise with faster readouts causing larger temperature variations in the on-chip amplifier which leads

98 Observations & Data Reduction 72 to a greater read noise per pixel (Howell 2006). With modern day detectors this source of noise is in most cases not dominant. Dark current Dark current is quantum mechanical property of the detector whereby electrons accumulate within a pixel due to thermal noise. As such, detectors are cooled to a constant temperature to limit this noise source. Dark current is not much of an issue for CCD detectors, however for near-ir detectors doing longer integrations, dark current can become a significant source of noise, warranting calibrations with dark frames. The dark current is expressed as σ dark = n pix N D t (2.10) in units of e /second/pixel where N D is the total dark count per pixel in units of electrons Shot noise The quantum nature of light causes the photons to arrive at the detector sporadically and uncorrelated with time. When the number of photons detected are sparse, such as for observations of faint objects, or when the exposure times are very short, different amount of photons are detected causing variations in the signal. This variation in the measured signal is known as shot noise. The probability of arrival is described by a Poisson distribution: Pois(n; k) = nk n! e n (2.11) which has a standard deviation of σ = n where n are the average number of events within a given time interval and k the number of events detected (number of electrons detected) The Signal-to-noise ratio The complete CCD equation describing an estimate of the signal-to-noise ratio (S/N), derived in Merline & Howell (1995), takes the following form:

99 Observations & Data Reduction 73 S N N ( ) N + n pix 1 + n (NS pix n B + N D + NR 2 + ) G2 σf 2 (2.12) where N is the total star counts (electrons), n pix the number of pixels used in integration of source, n B number of pixels used in background determination, N S total sky counts per pixel (electrons), N R read noise (electrons/pixel/read), G gain of CCD (electrons/adu) and σ f the uncertainty caused within the A/D converter. The fraction n pix /n B decreases with increasing resolution. As an example, consider a large diameter telescope using adaptive optics, which results in a seeing improvement from 1.0 to 0.1. In this scenario, this noise term would decrease by a factor 100 (not accounting for Airy rings) as the signal is preserved, since the sky background contribution diminishes due to an area reduction from 1.0 squared to 0.1 squared. When observing bright sources such as exoplanet host stars the dominant source (not accounting for systematic noise) is the object itself (see Shot noise 2.3.2) which allows Eq to be approximated as: S N N N = N (2.13) When limited by the sky background such as when looking at faint sources or during near-ir observations (or both), the term N S dominates giving: (shot noise from the sky) S N N ( ) (2.14) n pix 1 + n pix n B N S Once the S/N value has been measured it can be converted to magnitude errors using the relation: σ(m) = ±2.5 log (1 + N/S). (2.15)

100 Observations & Data Reduction Systematic noise Correlated noise which does not follow the noise properties associated with random noise and depart from a N improvement in the uncertainities for N number of measurements, is considered systematic noise. Time-correlated noise, sometimes referred to as red noise can have a profound effect on observational data and is often hard to account for in the final estimation of measurement uncertainties. This is because the systematic noise can be made up of multiple components which do not follow a clear deterministic model. For instance, an increasing airmass can lead to differential refraction effects, but also affect the shape of the PSF and FWHM values as the seeing worsens. There are several techinques in place for estimating the red noise contribution. One of these techniques is the timeaveraging method by (Pont et al. 2006), where the variance of time-averaged data for various bin sizes are calculated and compared to the scatter of the un-binned residuals. In the event where the noise is random and uncorrelated with time white noise, the scatter of the time-averaged bins should follow a N relation, and only depart form it if the data is affected by red noise (see to see how this method affects the uncertainties). There are also various other methods used to estimate the red noise contribution such as the wavelet method (Carter & Winn 2009a) and the residual-permuation method (Jenkins et al. 2002). To remove the red noise constribution, auxillary parameters such as airmass, FWHM, detector positions in conjuction with deterministic models (mainly polynomials and trigonometric functions) have been used. Recently there have been developments in alternative approaches such as blind extraction techniques based on principle component analysis (Waldmann et al. 2013) and Gaussian processes (Gibson et al. 2012). They differ in their use of auxillary parameters with the latter method using them whereas the former does not. The advantage of the methods is their move away from the parametric approach with the systematics model not having to be set a priori.

101 Chapter 3 Weather in the atmospheres of Brown Dwarfs 3.1 The brown dwarf atmosphere monitoring (BAM) project. I. The largest near-ir monitoring survey of L and T dwarfs Abstract Using the SofI instrument on the 3.5 m New Technology Telescope, we have conducted an extensive near-infrared monitoring survey of an unbiased sample of 69 brown dwarfs spanning the L0 to T8 spectral range, with at least one example of each spectral type. Each target was observed for a 2 4 hour period in the J s -band, and the median photometric precision of the data is 0.7%. A total of 14 brown dwarfs were identified as variables with min-to-max amplitudes ranging from 1.7% to 10.8% over the observed duration. All variables satisfy a statistical significance threshold with a p-value 5% based on comparison with a median reference star light curve. Approximately half of the variables show pure sinusoidal amplitude variations similar to 2MASSJ , and the remainder show multi-component variability in their light curves similar to SIMPJ It has been suggested that the L/T transition should be a region of a higher degree of variability if patchy clouds are present, and this survey was designed to test the patchy cloud model with photometric monitoring of both the L/T transition 75

102 Weather in the atmospheres of Brown Dwarfs 76 and non-transition brown dwarfs. The measured frequency of variables is % across the L7 T4 spectral range, indistinguishable from the frequency of variables of the earlier spectral types ( %), the later spectral types ( %), or the combination of all non-transition region brown dwarfs ( %). The variables are not concentrated in the transition, in a specific colour, or in binary systems. Of the brown dwarfs previously monitored for variability, only 60% maintained the state of variability (variable or constant), with the remaining switching states. The 14 variables include nine newly identified variables that will provide important systems for follow-up multi-wavelength monitoring to further investigate brown dwarf atmosphere physics Introduction The L, T, and Y-type brown dwarfs represent a link between the coolest stars and giant planets. Many brown dwarfs are even cooler than currently observable exoplanetary atmospheres (e.g. HR 8799b, HD b; Barman et al. 2011, Sing et al. 2009, 2011a). The recently discovered Y dwarfs (Cushing et al. 2011) approach the temperature of Jupiter. Since brown dwarfs never achieve a stable nuclear burning phase, they cool throughout their lifetimes, and temperature, rather than mass, is the dominant factor in defining the spectral sequence. As they cool, their atmospheres undergo changes in the chemistry and physical processes that sculpt their emergent spectra. While spectroscopy can be used to investigate atmospheric constituents and chemistry, photometric monitoring is an effective means to search for evidence of surface brightness inhomogeneities caused by cloud features, storms, or activity. The transition region from late-l to early-t encompasses a particularly interesting change in physical properties, as the atmospheres transform from dusty to clear over a narrow effective temperature range, and the observed infrared colours reverse from red to blue. This is predicted to be an effect of the formation and eventual dissipation of dusty clouds in brown dwarf atmospheres (Burrows et al. 2006; Chabrier & Baraffe 2000; Marley et al. 2002). Broadly, as brown dwarfs cool through the spectral sequence, the lower temperatures allow more complex molecules to form, resulting in condensate clouds. When the temperature is cool Based on observations made with ESO Telescopes at La Silla Observatory under programme ID 188.C-0493.

103 Weather in the atmospheres of Brown Dwarfs 77 enough, large condensate grains cannot remain suspended high in the atmosphere and sink below the observable photosphere, allowing methane and molecular hydrogen to become the dominant absorbers. Although there are several existing models for condensate cloud evolution, most cannot easily explain the rapid colour change from red to blue over the L-to-T transition. A systematic survey of variability in brown dwarfs including both L/T transition objects and comparison hotter/cooler objects is required to search for differences in the structure of condensate clouds in this important regime. Existing photometric monitoring campaigns of brown dwarfs have been conducted at different wavelengths: optical bands (e.g. Tinney & Tolley 1999 and Koen 2013), near-ir bands (e.g. Artigau et al. 2003, Khandrika et al and Buenzli et al. 2013), mid-ir (e.g. Morales-Calderón et al. 2006), and radio frequencies (e.g. Berger 2006). From small (< 20 objects) initial samples of ultracool field dwarfs, frequencies of variables ranged from 0% to 100% (e.g. summary in Bailer- Jones 2005), and results from larger studies ( 25 objects) have measured the frequency of variables to be in the range of 20% to 30% (e.g. Buenzli et al. 2013; Khandrika et al. 2013). Examples of objects that vary in multiple wavebands have been identified (e.g. 2MASS J Buenzli et al. 2012; Clarke et al. 2008, SIMP J Artigau et al. 2009, 2MASS J Radigan et al. 2012), as well as objects recorded as variable in one wavelength range, but not another (e.g. 2MASS J , Koen et al. 2004). A small set of variable sources have been monitored contemporaneously at multiple wavelengths, with the combined results being used to infer the vertical extent of atmospheric features and to investigate atmospheric circulation patterns (e.g. Buenzli et al. 2012). Given the unique probe of the atmospheric structure that multi-wavelength observations provide, it is essential to identify a larger set of known variables across a broad range of effective temperatures. Most monitoring programs have involved observation sequences spanning a few hours, but some studies have searched for longer timescale variations (e.g. Enoch et al. 2003; Gelino et al. 2002). A time scale of a few hours is well-matched to a search for rotation-modulated variability, since expected rotation periods are 2 12 hours for L and T dwarfs, considering the range of measured v sin i values (10 60 km/s for L dwarfs and km/s for T dwarfs Zapatero Osorio et al. 2006) and the radius of the M objects from evolutionary models at the age of the field (Baraffe et al. 2003). Periodogram analysis of some variables

104 Weather in the atmospheres of Brown Dwarfs 78 has shown clear peaks associated with periods in the range of 2 8 hours (e.g. Clarke et al. 2008; Radigan et al. 2012) which is consistent with an atmospheric feature rotating into and out of view. Other variables exhibit multi-component light curves (e.g. Artigau et al. 2009) that are suggestive of a rapid evolution of atmospheric features. An unresolved BD binary system which consists of two BDs each with a different spectral type, can mimic a single BD with a spectral type somewhere between the individual BDs. This can lead to an incorrect spectral typing which may alter the statistics on the number of variables as a function of spectral type. A BD binary pair with only one variable BD will cause an underestimate of the measured variability amplitude if the binary system is unresolved as the nonvariable component of the system dilutes the variability signal. As such, binaries play an important role in both the frequency and amplitudes of brown dwarfs. BD binary systems are typically found using high-resolution imaging (adaptive optics or HST) (e.g. Burgasser 2007), radial velocity variations (e.g. Joergens 2006b) or by carefully studying the spectra of possibly unresolved BD binary systems which may lead to the identification of spectroscopic binaries (e.g. Burgasser et al. 2010). The direct imaging method is most sensitive to BD binary separations greater than 3 AU whereas, RV measurements are most sensitive to close in binaries (typically 0.6 AU) (Joergens 2008). The binary frequency is observed to decrease as a function of primary mass with 60 % of solar type stars being found in binary systems, % for M-dwarfs and 15 % for BDs (see Dhital et al and references therein). The peak of the BD binary separation distribution is found at 4 7 AU (Allen 2007; Maxted & Jeffries 2005) although the width of the distribution is still loosely constrained, something which orbital characterisation and the detection of more spectral binaries will help constrain (Duchêne & Kraus 2013). All the known binary BDs in the BAM sample are unresolved. To investigate the variability of brown dwarfs across the full L-T spectral sequence, we have performed a large-scale J s -band photometric monitoring campaign of 69 field brown dwarfs with the SofI instrument on the 3.5 m New Technology Telescope (NTT). This survey is a part of the BAM (Brown dwarf Atmosphere Monitoring) project. In Section 3.1.3, the properties of the sample, including magnitudes, spectral types, and companions are summarised. Details of the observations are reported in Section 3.1.4, followed by the data reduction procedure,

105 Weather in the atmospheres of Brown Dwarfs 79 and methodology used to characterise each target as variable or constant in Section Section presents the results of the program and a comparison to previous variability studies. Finally, we discuss the sensitivity of the BAM survey and investigate possible correlations between variability and various observables such as spectral type, colour and binarity in Section The results are summarized in Section The BAM sample The 69 objects in the BAM sample were drawn from the brown dwarf archive (dwarfarchives.org) and were selected to span the full sequence of L- and T- spectral types from L0 to T8. An equal proportion of targets with spectral types above, across and below the L/T transition region were included. In this paper, we consider the L-T transition to range from L7 T4, following Golimowski et al. (2004). Spectral types including a fractional subtype have been rounded down - for example, an L6.5 is considered L6 for the statistics. For the 48 targets with parallax measurements (e.g. Dupuy & Liu 2012; Faherty et al. 2012), a colourmagnitude diagram was constructed and is shown in Figure 3.1. The histogram of target spectral types and a plot of the colour as a function of spectral type are shown in Figure 3.2. The spectral types are based on IR spectroscopy for 54 targets and on optical spectroscopy for the remaining 15 targets that lacked an IR spectral classification. The spectral types, parallaxes, and apparent 2MASS magnitudes of the targets are listed in Table 3.1 for L dwarfs and Table 3.2 for T dwarfs. Additional factors that influenced the target selection were the magnitudes and coordinates. To obtain high signal-to-noise individual measurements, the targets were limited to objects with magnitudes brighter than J 16.5 mag. To avoid observations at high airmass, the target declinations were limited to South of +20 degrees. Pairs of targets were observed for sequences of 2 to 4 hours, which also impacted the range of target coordinates observed each observing run. The majority of the sample, 47 targets, have been observed in programs designed to detect binary companions with radial velocity variations (Blake et al. 2010), or spectra showing features of different spectral types (Burgasser et al. 2010), or high angular resolution imaging (i.e. Bouy et al. 2003; Burgasser et al. 2006, 2003a, 2005; Looper et al. 2008; McCaughrean et al. 2004; Reid et al. 2008, 2006).

106 Weather in the atmospheres of Brown Dwarfs L0-L6 L7-T4 T5-T8 12 M J,2MASS (mag) (J-K) 2MASS (mag) Figure 3.1: Colour-magnitude diagram of the M-L-T spectrum (small grey circles). All brown dwarfs with known parallax in the BAM sample are overplotted, with red representing the L dwarfs, yellow the L/T transition dwarfs, and blue the T dwarfs (see Table 3.1 and 3.2). Half spectral types have been rounded down in the study. The photometry and parallaxes for the field M-L-T objects are from Dupuy & Liu (2012). BD Number Targets 23 Targets 23 Targets L0 L2 L4 L6 L8 T0 T2 T4 T6 T8 Spectral Type (J-K) 2MASS (mag) L0 L2 L4 L6 L8 T0 T2 T4 T6 T8 Spectral Type Figure 3.2: Diagram on the left shows a histogram of the sample across their respective spectral classes, whilst on the right is a colour-colour diagram showing the J-K colours of the same (coloured circles) overplotted on the full brown dwarf L-T spectral sequence (small grey circles). The L/T transition is indicated by the dashed lines defined in Golimowski et al. (2004).

107 Weather in the atmospheres of Brown Dwarfs 81 Based on the companion search programs reported in the literature, a total of 12 targets are members of spatially resolved binary pairs, and the results of all the binary searches are reported in Table 3.1 and 3.2. The proportion of binaries in this sample is comparable to the overall brown dwarf binary frequency (Burgasser et al. 2003a), indicating that the sample is not biased in the level of multiple systems included. All of the binaries in the sample have separations less than the seeing limit, so the photometric measurements in this study record the combined flux from both components. A variable brown dwarf that is part of an unresolved binary system can be more difficult to detect, as the variability is diluted by the non variable companion. Previous observations designed to search for photometric variability have been reported for approximately half the sample 34 targets and cover optical (Gelino et al. 2002; Koen 2013), near-ir (Buenzli et al. 2013; Clarke et al. 2008; Enoch et al. 2003; Khandrika et al. 2013; Koen et al. 2004, 2005), and radio (Berger 2006) wavelengths. It is important to note that the different variability monitoring studies apply different criteria to categorise a target as variable or constant, and a range of observation wavelengths have been employed. Most of the previous monitoring has been conducted over timescales of hours similar to this program, though a few studies covered longer timescales with lower cadence measurements (e.g. Gelino et al. 2002, Enoch et al. 2003) Observations The observations took place from 4-11 October 2011 and 3-9 April 2012 with the SofI (Son of ISAAC) instrument (Moorwood et al. 1998) mounted on the NTT (New Technology Telescope) at the ESO La Silla observatory. Observations were performed in the large field imaging mode that has a pixel scale of px 1 and a field-of-view of During the first observing run, some of the targets were observed in both the J s -band and K s -band, but only the J s -band was used during the second run. As a consequence, six of the targets from the first run have J s -band data with lower cadence. The J s filter ( µm) was used to avoid contamination by the water band centred at 1.4 µm that would have otherwise affected the photometry. An increase in the telluric water column would have caused an anti-correlation between the brightness of the brown dwarfs and the reference stars in the J-band, since an increase in the water column will decrease

108 Weather in the atmospheres of Brown Dwarfs 82 the flux from the reference stars to a greater extent compared to the brown dwarfs that have deep intrinsic water bands. The J s data should not suffer from this effect. Three sets of two target fields were observed most nights, alternating between each target roughly every 15 min over a 3.5 hour window. This procedure allowed six targets to be observed every night. During clear conditions, the observations had a detector integration time (DIT) of 5s, with three DITs (NDIT) taken and averaged together with about 25 exposures in each observing block. During poorer conditions, such as the presence of cirrus clouds, and for fainter objects, the exposure times were increased. The flux was kept below 10,000 ADUs for the brightest targets in the field to prevent any non-linearity effects.

109 Weather in the atmospheres of Brown Dwarfs 83 Table 3.1: L dwarf Sample. Target Name Spectral Parallax J 2MASS Binary/ Instrument References Type (mas) (mag) Single 2MASS J L3.5* ± S SpeX spectra K08, BC10 2MASS J L2* ± R08 2MASS J L0* ± R08 2MASS J L ± ± K07, D07 DENIS J L ± ± 0.03 B (409 mas) HST imaging R06, K04, D02, B03 2MASS J L ± K07 2MASS J L8* ± K08, R08 2MASS J L7* 72.9 ± ± S HST imaging K08, F12, R08 S SpeX spectra BC10 2MASS J L7* ± C07, K08 2MASS J L5* ± R08 2MASS J L ± R08, B06 2MASS J L6.5* ± ± S HST imaging C03, F12, R06 2MASS J L2* 78.5 ± ± S HST imaging C03, F12, R06 2MASS J L ± S radial velocity C03, W03, BCW10 2MASS J L5* 83.9 ± ± S HST imaging R08, F12, R06 2MASS J L5* ± ± S HST imaging C03, And11, R06 S radial velocity BCW10 S SpeX spectra BC10 2MASS J L7* ± 0.03 B (730 mas) HST imaging R08, R06 2MASS J L ± K04 2MASS J L4* 54.8 ± ± Giz02, And11 2MASS J L6* 59.8 ± ± C03, F12 2MASS J L ± F07, B06 2MASS J L ± ± S SpeX spectra K04, F12, BC10 2MASS J L ± ± 0.03 B (264 mas) HST imaging D97, K04, D12, B03 2MASS J L ± S HST imaging Giz00, B06, R08 S radial velocity BCW10 2MASS J L ± ± S SpeX spectra F00, K04, V04, BC10 2MASS J L ± ± S HST imaging R00, K04, D02, R06 2MASS J L ± ± 0.07 S HST imaging K99, B06, D02, B03 2MASS J L5* 66.3 ± ± S HST imaging R08, F12, R06 SDSS J L ± ± S SpeX spectra C06, S13, BC10 2MASS J L ± ± B (130 mas) HST imaging Ken04, D12, RL06 2MASS J L ± 0.03 B (120 mas) HST imaging K07, R08 2MASS J L0* 58.6 ± ± R08, F12 Note: *Spectral classification using optical data References: Andrei et al. (2011)[And11], Bouy et al. (2003) [B03], Blake et al. (2010) [BCW10], Berger (2006) [B06], Burgasser et al. (2010) [BC10], Cruz et al. (2003) [C03], Chiu et al. (2006) [C06], Cruz et al. (2007) [C07], Dahn et al. (2002) [D02], Deacon & Hambly (2007) [D07], Delfosse et al. (1997) [D97], Dupuy & Liu (2012)[D12], Folkes et al. (2007)[F07], Faherty et al. (2012) [F12], Fan et al. (2000) [F00], Gizis et al. (2000) [Giz00], Gizis (2002) [Giz02], Kendall et al. (2004) [Ken04], Kendall et al. (2007) [K07], Kirkpatrick et al. (1999)[K99], Kirkpatrick et al. (2008)[K08], Knapp et al. (2004) [K04], Reid et al. (2000) [R00], Reid et al. (2006) [R06], Reid et al. (2006) [RL06], Reid et al. (2008) [R08], Smart et al. (2013)[S13], Vrba et al. (2004) [V04].

110 Weather in the atmospheres of Brown Dwarfs Data Reduction and Photometry Processing the images For each image, basic data reduction steps consisting of correcting for the dark current and division by a flat field and sky subtraction were applied. Developing flat field images for the NTT/SofI instrument involved generating two different flats, a special dome flat and an illumination correction flat as documented by the observatory. The dome flat requires observations of an evenly illuminated screen with the dome lamp turned on and off in a particular set sequence. To correct for low frequency sensitivity variations across the array that are not completely removed by the dome flat, an illumination correction was applied. By observing the flux from a standard star in a grid pattern across the array, a low order polynomial was fitted to the flux measurements, allowing large scale variations across the array to be characterised and removed. Flat field images were produced using the IRAF 1 scripts provided by the observatory 2. As the flat fields are documented to be extremely stable over several months, a single set of flat fields were used for all the targets in a given run. For the SofI instrument, the dark frames are a poor estimate of the underlying bias pattern, which varies as a function of the incident flux. Consequently, the darks are subtracted from the science frames through the computation of a sky frame, which also removes the sky background from the science data. Sky frames were generated by median combining the dithered science frames. The final calibration step involved measuring the offsets between the individual images and aligning all the science frames. The aligned frames within each 15 min interval were subsequently median combined. We compared the photometric uncertainties on the median combined images calculated using IRAF, to the standard deviation of the unbinned images within each bin. For most objects, the two methods for calculating uncertainties gave very similar results. The IRAF uncertainties on the median combined images were used for all the objects for consistency. Median combining the images before performing photometry rather than measuring the individual frames had the advantage of improving the centring, measurements 1 IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. 2 sofi_scripts.html

111 Weather in the atmospheres of Brown Dwarfs 85 of the full width at half maximum (FWHM), and the photometry of the fainter comparison stars in the field.

112 Weather in the atmospheres of Brown Dwarfs 86 Table 3.2: T dwarf Sample. Target Name Spectral Parallax J 2MASS Binary/ Instrument References Type (mas) (mag) Single 2MASS J T ± ± B04, B06, F12 2MASS J T ± ± 0.07 T05, B06, D12 SIMP J T ± 0.03 A06 2MASS J T ± 0.05 S HST imaging B03, BK06 2MASS J T ± ± S HST imaging B02, B06, V04, BK06 SDSS J T ± ± B (160 mas) HST imaging G02, B06, V04, B05 2MASS J T ± L07 2MASS J T ± ± S HST imaging B03, F12, B06, BK06 2MASS J T ± ± S HST imaging B00, B06, D02, BK03 2MASS J T ± ± L07, F12 DENIS J T6 203 ± ± A10 2MASS J T ± ± T05, B06, B08 2MASS J T ± ± 0.117?B (weak candidate) SpeX spectra T05, F12, B06, BC10 2MASS J T ± ± L07, F12 2MASS J T ± ± B (172 mas) HST imaging L00, B06, T03, BK06 2MASS J T ± ± T05, B06, D12 2MASS J T ± ± 0.071?B (weak candidate) SpeX spectra H02, F12, B06, BC10 2MASS J T ± ± S HST imaging B99, B06, T03, BK06 2MASS J T ± ± B (282 mas) HST imaging B99, B06, T03, BK03 2MASS J T ± B04, B06 2MASS J T ± ± S HST imaging L00, B06, D02, BK06 2MASS J T ± ± B (130 mas) AO imaging L07, D12, L08 2MASS J T ± ± 0.079?B (strong candidate) SpeX spectra A11, F12, BC10 2MASS J T ± ± S SpeX spectra K04, F12, B06, BC10 2MASS J T ± ± B (65 mas) HST imaging B02, B06, T03, BK03 2MASS J T ± ± S HST imaging B02, B06, T03, BK03 2MASS J T ± ± B (349 mas) HST imaging B02, B06, D12, BK06 2MASS J T ± ± S HST imaging S99, B06, T03, BK06 2MASS J T ± ± B04, F12, B06 SDSS J T ± ± 0.04* S SpeX spectra K04, F12, B06, BC10 2MASS J T ± ± 0.118?B (weak candidate) SpeX spectra C06, D12, BC10 B (100.9 mas) AO imaging S11 2MASS J T ± ± 0.049?B (strong candidate) SpeX spectra R08, B06, S13, BC10 2MASS J T ± ± E05, F12, B06 2MASS J T ± ± S HST imaging B03, F12, B06, BK06 ULAS J T ± 0.04* S10, B10 2MASS J T ± B04, B06 2MASS J T ± ± S HST imaging B02, B06, S13, BK03 Note: *MKO to 2MASS conversion using transformations from Stephens & Leggett (2004). References: Albert et al. (2011) [A11], Artigau et al. (2006) [A06], Artigau et al. (2010) [A10], Berger (2006) [B06], Bouy et al. (2003) [B03], Burgasser et al. (1999) [B99], Burgasser et al. (2000) [B00], Burgasser et al. (2003b) [B02], Burgasser et al. (2003a) [BK03], Burgasser et al. (2004) [B04], Burgasser et al. (2005) [B05], Burgasser et al. (2006) [BK06], Burgasser et al. (2008) [B08], Burgasser et al. (2010) [BC10], Burningham et al. (2010) [B10], Chiu et al. (2006) [C06], Dahn et al. (2002) [D02], Ellis et al. (2005) [E05], Faherty et al. (2012) [F12], Gelino et al. (2002) [G02], Hawley et al. (2002) [H02], Knapp et al. (2004) [K04], Leggett et al. (2000) [L00], Looper et al. (2007) [L07], Looper et al. (2008) [L08], Reid et al. (2008) [R08], Scholz et al. (2003) [S03], Scholz et al. (2003) [S10], Stumpf et al. (2011) [S11], Smart et al. (2013) [S13], Strauss et al. (1999) [S99], Tinney et al. (2003) [T03], Tinney et al. (2005) [T05], Vrba et al. (2004) [V04].

113 Weather in the atmospheres of Brown Dwarfs Generating the light curves Aperture photometry was carried out using the APPHOT package in IRAF. A median value of the FWHM was measured per image using all the stars in the field-of-view. A range of aperture radii were explored and the size of 1.5 FWHM was selected, as it minimised the root-mean-square (RMS) scatter of the reference star light curves that were created by dividing each reference star by the weighted mean of the remaining reference star light curves. The aperture was kept constant for all the stars in a single image, but was allowed to vary between individual images to account for variations in seeing. The variable aperture also yielded higher signal-to-noise measurements compared to a constant aperture, which would otherwise cause a loss in the flux measured within the aperture during poorer seeing conditions. We checked each target field to ensure that the photometry was not impacted by nearby astrophysical sources. The steps taken to generate the target light curves in the survey are given in the following list: For each target, a list of reference star candidates was generated by considering all stars visible in the field of view, discarding stars with peak counts less than 20 ADUs or greater than 10, 000 ADUs. These limits were imposed to ensure enough signal was present to accurately centre the aperture around the object and to ensure that none of the reference stars were in the non-linear regime of the detector. Reference candidates were trimmed by selecting up to 15 of the reference stars with the most similar brightness to the target. Candidate reference star light curves were calculated by dividing each reference star by a weighted mean of the remaining reference stars. Candidate reference stars with light curves exhibiting a standard deviation greater or equal to the median standard deviation for all reference star candidates were removed. A master reference light curve was subsequently created by median combining the normalised light curves of all the qualifying reference stars. The final target light curve was produced by dividing the target brown dwarf flux by the weighted mean of all the qualifying reference stars. The light

114 Weather in the atmospheres of Brown Dwarfs 88 Number Target Photometric Uncertainty, Q (%) Figure 3.3: Target photometric uncertainty of the survey defined as the median value of the final target light curve uncertainties. The median target photometric uncertainty is 0.7%. curve was normalised by dividing the light curve by the median flux value of the light curve. The target and reference star light curves were all airmass de-trended by dividing the light curves by a second order polynomial fit to the relative flux of the master reference as a function of airmass. The number of reference stars used for each target is given in Table 3.3 and Table 3.4, with six to eight references being typical (with the fewest number of reference stars being three). The automatic selection process was applied uniformly throughout the entire sample of objects. The uncertainties were calculated using IRAF. The target photometric uncertainty (Q) is defined as the median value of the target light curve uncertainties. A histogram of the Q values for each object is shown in Figure 3.3, and the value for all targets are listed in Table 3.3 and Table 3.4. The median Q value for the entire survey is 0.7%.

115 Weather in the atmospheres of Brown Dwarfs 89 BD Number p-value (%) Figure 3.4: p-value histogram of the full brown dwarf sample. The objects in the first bin includes 16 targets with p-value 5%, and three targets with p-values from 5 10%. Of the 16 targets with p-value 5% listed in Table 3.3, two targets are not listed since they failed the robust criterion ( η 1). The large number of objects in the last two bins (80 to 100) is suggestive of conservative errorbars.

116 Weather in the atmospheres of Brown Dwarfs 90 Table 3.3: Variables identified in this study. Object Spectral Type Obs. Dur. (hours) Refs. DOF χ 2 ν η Q (%) p-value (%) Amplitude (%) Variables with p-value 5% and η 1.0 2MASS J L ± 1.2 2MASS J L ± 0.9 2MASS J L ± 1.2 2MASS J L ± 0.5 2MASS J L ± 1.6 2MASS J L ± 1.1 2MASS J L ± 0.5 2MASS J L ± 0.7 2MASS J T ± 1.1 2MASS J T ± 0.5 SIMP J T ± 0.6 2MASS J T ± 0.7 2MASS J T ± 1.3 2MASS J T ± 0.5 Variables with 5% < p-value 10% and η 1.0 DENIS J L ± 0.6 2MASS J L ± 1.9 2MASS J T ± 1.1 Notes: These peak-to-trough amplitudes are calculated as the difference between the minimum and maximum points in the light curve. In some cases, these might represent the lower limit of the true amplitude, especially for brown dwarfs which exhibit variability on longer time scales.

117 Weather in the atmospheres of Brown Dwarfs Identifying variables The significance of the variations were assessed in comparison to two criteria. For the first assessment, the final target light curve was compared against a flat line using the reduced robust median statistic ( η) (Enoch et al. 2003). The definition of η is expressed as η = 1 N F i median( F ) d σ i (3.1) i=1 where d defines the number of free parameters and σ i, the uncertainty on each photometric measurement in the final target light curve. For the second assessment, the reduced chi squared (χ 2 ν) value for each target light curve was calculated relative to the master reference light curve. The definition of χ 2 ν is expressed as χ 2 ν = 1 ν N (O i E i ) 2 i=1 σ 2 i (3.2) where ν is the degrees of freedom, O i is the final target light curve, E i is the master reference light curve and σ i is the uncertainty on the final target light curve and master reference light curve added in quadrature. Astrophysical variability was better determined calculating χ 2 ν relative to the master reference light curve instead of a straight line, which was more prone to classifying variable conditions over intrinsic variability. We make use of the χ 2 ν to estimate the cumulative distribution function and thus the p-value for each final target light curve. The p-value is the probability that the final target light curve is the same as (p-value > 10%) or different from (p-value 10%) the master reference light curve. In Figure 3.4, we plot the histogram of the calculated p-values for the full sample, and the large number of objects in the first bin gives an indication of the variables in the survey. The first bin contains 16 objects with p-value 5%, and the level of false positives expected with an equivalent p-value is 3 to 4 objects (5%) for a sample of 69 targets. For the identification of variables, both p-value and an η thresholds were applied. The number of targets with p-value 5% but η > 1 was two, which is similar to the level of expected false positives. The excess of targets in the last two bins of Figure 3.4 suggests that the uncertainties for the sample are conservatively estimated.

118 Weather in the atmospheres of Brown Dwarfs 92 The p-value is the probability, under the assumption that we detect no variability (our null hypothesis), of observing variability greater or equal to what was observed in the master reference light curve. The survey has 39 targets satisfying the criterion of η 1 and 16 targets with p-value 5%. Objects classified as variable in this study satisfied two criteria, defined by p-value 5% and η 1, and they are listed in Table 3.3. Candidate variables with a less restrictive p-value 10% and η 1 are also listed in Table 3.3. The min-to-max amplitudes of the variable objects were calculated as the difference between the highest and the lowest point in the light curve, using the uncertainties on these two points to calculate the uncertainty on the amplitude. Using this method to calculate the amplitude is dependent on how the data is binned, with the unbinned data showing larger amplitude variations. The amplitudes listed in Table 3.3 use the more conservative estimate from binned data. For objects with periods larger than the duration of observations, the amplitude is likely an underestimate, as the entire period is not observed. An example of a target with a known variable period exceeding the observation timescale is 2M2139, and the reported amplitude in this study is lower than longer timescale results (Radigan et al. 2012). Due to the limited duration and cadence of the observations, it is not possible to measure the periods of the variables in the BAM study Results of the BAM survey The primary result from the BAM survey is the identification of a set of 14 variable brown dwarfs with p-value 5% and a further three candidate variables with 5% < p-value 10% (see ). For the remaining analysis, we only consider the p-value 5% variables. The BAM variables appear to show two morphologies. The first type of light curve shows pure sinusoidal trends, akin to 2M2139 (Radigan et al. 2012). Variables like 2M0050, 2M0348, 2M1010, and possibly 2M2255 appear to have sinusoidal light curves. The second group consists of targets that appear to display multi-component variations in their light curves akin to SIMP0136 (Artigau et al. 2009; Metchev et al. 2013). SIMP0136 shows remarkable evolution in its features over multiple epochs, possibly caused by rapidly varying cloud features (Metchev et al. 2013). Objects with light curves similar to SIMP0136 object, such as 2M0106, 2M0439, 2M0835, 2M1126, 2M1207, 2M1300 are interesting for future follow up, to confirm whether or not they also

119 Weather in the atmospheres of Brown Dwarfs 93 Relative Flux Relative Flux Relative Flux Relative Flux Relative Flux L0 J L5 J L6.5 J J T J T Time (Hours) L3 L5.5 L6.5 T2.5 J J J J T7 J Time (Hours) L J L6 J T J T J Time (Hours) Figure 3.5: Final target light curves of the 14 variable objects (blue points) with a p-value 5% and η 1.0 together with the master reference light curves (yellow points). The uncertainties on the variable light curve incorporates the uncertainties in the master reference light curve.

120 Weather in the atmospheres of Brown Dwarfs 94 Relative Flux J L Time (Hours) T7.5 J Time (Hours) J T Time (Hours) Figure 3.6: Final target light curves of the candidate variables (larger blue points) with 5% < p-value 10% and η 1.0 together with the master reference light curves (yellow smaller points). Relative Flux Relative Flux Relative Flux J Q =0.37 J Q = J Q = Time (Hours) J Q = J Q = J Q = Time (Hours) J Q = J Q = J Q = Time (Hours) Figure 3.7: Final target light curves of a subset of constant objects in this survey (larger blue points) with the master reference light curves (yellow smaller points). The target photometric uncertainty decreases from top to bottom and includes the light curve with the best photometry (top left) and light curve with the worst photometry (bottom right).

121 Weather in the atmospheres of Brown Dwarfs 95 show rapidly evolving light curves. Finally, the light curve of 2M0358 may be a fast rotating variable, since 2M0358 appears to oscillate through more than one cycle within the limited timespan of the BAM monitoring. The light curve of 2M2228 shows similar short time scale variations as 2M0358 and was previously found to be variable with a period of P= hours by Clarke et al. (2008). Final target light curves for the 14 BAM variables and the associated comparison master reference light curves are shown in Figure 3.5. Similar plots for the candidate variables are given in Figure 3.6. The amplitudes and p-values are reported in Table 3.3. Representative light curves of nine constant targets with a range of photometric qualities are shown in Figure 3.7. These light curves show the full range of the data quality for brown dwarfs of similar brightness to the variables identified in the study. The constant light curves are not all flat, however their variations are not statistically distinct from their associated master reference. The constant targets do not satisfy the two separate criteria used to identify the variables (specified in section ) which require the final target light curve to be distinct from the master reference light curve (p-value) and a flat line ( η). The p-values for constant sources are given in Table 3.4. Since the p-value 5% cutoff is a statistical measure, there remains a likelihood of a contamination level of 3 4 false variables that are statistical fluctuations, 5% of the entire sample. Continued monitoring of the variables should help identify false positives Comparison of variables with previous studies This J s -band SofI program is the largest uniform monitoring survey conducted in the near-ir. Several previous surveys have targeted smaller sample sets (e.g. Buenzli et al. 2013; Clarke et al. 2008; Enoch et al. 2003; Girardin et al. 2013; Khandrika et al. 2013; Koen et al. 2004, 2005) or searched in different wavelengths such as I-band (e.g. Gelino et al. 2002; Koen 2004, 2013). Apart from results of the study by Koen (2013), previous surveys have typically targeted fewer than 25 objects and detected variability frequencies of 30% in their sample sets, with a significant amount of overlap in the target samples used in different studies (Khandrika et al. 2013). The BAM sample was designed to uniformly cover the L- T spectral range (see Figure 3.2) and includes 35 brown dwarfs that have not been

122 Weather in the atmospheres of Brown Dwarfs 96 previously monitored in different surveys. There are nine new BAM variables, six of which have not been previously monitored for variability 2M0050, 2M0106, 2M0358, 2M1010, 2M1207 and 2M2255. The survey has three variables that were previously found to be constant, and found nine brown dwarfs previously classified as variable to be constant. Finally, there are five variables that were found to vary in the literature and in this BAM study. A synopsis of the variables in the BAM and previous surveys is presented in Table 3.5. These objects are used to investigate the persistence of variability in section Table 3.6 presents the constant brown dwarf sample in the BAM study. These are targets that were monitored in previous surveys and were found to be constant in the literature and in this study. In the following two subsections, we compare our results with literature measurements for the variables identified in this sample and in previous work BAM Variables In Table 3.5, we present information for all the targets that were considered variable, either in this BAM study or in the literature. Three of the BAM variables 2M0348, 2M0439 and 2M1126 were identified as constant brown dwarfs in prior surveys but appear to be variable in this survey. A further five brown dwarfs SIMP0136, 2M0835, 2M1300, 2M2139 and 2M2228 were confirmed to be variable both in this study and in the literature. Of these five, SIMP0136, 2M2139 and 2M2228 were previously found to vary in the near-ir, similar to this study. The other two variables 2M0835 and 2M1300 were originally measured to vary in the I c band, and also display multi-component variations at near-ir wavelengths. Amongst the known variables with measured periods (from previous studies), only 2M2139 and 2M1300 have periods longer than the duration of the BAM monitoring data (> 7 hours, and 238 hours, respectively). The latter period is much longer than the expected rotation for a brown dwarf (Zapatero Osorio et al. 2006), which indicates that the periodic feature might not be related to the rotation of the brown dwarf (Gelino et al. 2002). The three remaining targets with previously measured periods - SIMP0136, 2M0835 and 2M were monitored in this study with a time span greater than one of their rotational periods. All three objects that we monitored over an entire period had amplitudes consistent with what has been previously published.

123 Weather in the atmospheres of Brown Dwarfs Variables in previous studies not confirmed with BAM There are nine targets from the BAM sample that have been previously reported as variable, but were found to be constant in this survey. These sources are listed in Table 3.5, with a summary of the previous results pertaining to variability, including the observation wavelength and any notes on the amplitudes and timescales of the variations in brightness. One of these nine variables from literature 2M0228 has only been monitored in the optical. The remaining eight variables exhibited modulations in the near-ir. 2M0559, 2M0624, DENIS0817 and 2M1624 were found to have small amplitude variations in the Buenzli et al. (2013) survey carried out using the HST grism data. In the HST survey, 2M1624 showed variability in the water band ( µm) but was found to be constant at J-band wavelengths. Similar to other ground based surveys that found some of these targets constant, this BAM survey likely does not have the photometric sensitivity necessary to confirm the HST variables, nor is it possible to monitor the water bands from the ground. Another four targets SDSS0423, 2M0939, 2M1534 and 2M2331 also appear constant in the data. The photometric uncertainties on SDSS0423 and 2M2331 are too large to confirm their lower amplitude variability of 0.8% and 1.2%, respectively. Despite 2M0939 having been observed as a variable in the K band with an amplitude of 3.1% (Khandrika et al. 2013), we are unable to confirm any variability in J s with the BAM observations. 2M1534 was detected to vary in the JHK s bands initially in (Koen et al. 2004), but was constant in a later epoch (Koen et al. 2005). Koen (2013) further discounts the likelihood of detecting short period variability in 2M1534, but maintains that the target likely varies on the timescale of a few days. The reported amplitudes in the H-band and K-band are below the detection threshold in the data for this target Discussion The sensitivity of the BAM survey To obtain an estimate of the variability frequency for brown dwarfs across spectral types, it is essential to quantify the sensitivity of the data to detecting different amplitudes of variability. We estimate the sensitivity to variables of a certain amplitude as three times the target photometric uncertainty of each final target light curve. This places a limit on the minimum amplitude required for a detection

124 Weather in the atmospheres of Brown Dwarfs 98 Table 3.4: Limits on constant targets in this survey. Object Spectral Type Obs. Dur. [hours] Refs. DOF χ 2 ν η Q (%) p-value (%) 2MASS J L MASS J L MASS J T MASS J L MASS J L MASS J L MASS J L MASS J L MASS J L MASS J T SDSS J T MASS J L MASS J T MASS J T MASS J L MASS J T MASS J L MASS J T DENIS J T MASS J L MASS J T MASS J T MASS J L MASS J T MASS J T MASS J T MASS J L MASS J T MASS J L MASS J T MASS J T MASS J L MASS J T MASS J L SDSS J T MASS J T MASS J T MASS J T MASS J T MASS J T MASS J L MASS J T MASS J L SDSS J L SDSS J T MASS J T MASS J T MASS J L ULAS J T MASS J L MASS J T MASS J T above a certain statistical significance threshold. The proportion of the sample that is sensitive to a given variability amplitude is shown as a function of amplitude in Figure 3.8. As shown in Figure 3.8, the BAM survey is capable of detecting any object in the sample showing a peak-to-trough amplitude 2.3% during the duration of the observations. The detection probability continues to decrease with decreasing amplitude with a sensitivity of 50% occurring for variables with a 1.7% amplitude. Given that the full BAM sample is sensitive to variables with amplitudes 2.3%, Table 3.7 quantifies the frequency of variability for different subsets of spectral types using an amplitude cutoff of 2.3% and p-value 0.05; this level includes all but one BAM p 0.05 variable. Figure 3.9 shows how the variability frequency (considering all spectral types) varies as a function of amplitude to account for the declining proportion of the sample that is sensitive to lower amplitude variables.

125 Weather in the atmospheres of Brown Dwarfs 99 Table 3.5: Summary of variable sources. Target Name Band Variable/Constant References Notes New variables from this study with no prior observations 2MASS J Js V 2MASS J Js V 2MASS J Js V 2MASS J Js V Candidate Variable (p-val= 6.1%) 2MASS J Js V 2MASS J Js V 2MASS J Js V New variables previously categorised as constant DENIS J Ic C K13 Candidate Variable (p-val= 7.9%) Ks C E03 < 3% 8.46 GHz C B06 < 30µJy 2MASS J J C C08 < 10 mmag, periodic 2MASS J Ic C K13 Ic C K GHz C B06 <42µJy 2MASS J Ic C K13 possibly periodic Literature variables confirmed as variable in this study SIMP J JK V A09, Ap13 J = 4.5%, P = 2.39 ± 0.05 hr 2MASS J Ic V K04, K13 Ic=10-16 mmag, P=3.1 hr 8.46 GHz C B06 < 30µJy 2MASS J J V A03 J = ± mag Candidate Variable (p-val= 9.3%) 8.46 GHz C B06 < 111µJy Z06 2MASS J Ic C K13 I V G02 P=238±9hr 8.46 GHz C B06 < 87µJy J + K C Kh13 J < 1.1%, K < 1.7% Ic C K05 JHKs C KMM04 2MASS J JHKs V R12, Ap13 (J,H,K)=(0.3, 0.18, 0.17) mag, P = 7.721±0.005 hr J + K V Kh13 J = 6.7%, C at K < 8% 2MASS J J V C08, Bu12 J = 15.4 ± 1.4 mmag, P=1.43±0.16hr 8.46 GHz C B06 < 30µJy Objects with reported IR variability measured as constants in this study SDSS J Ic C K13 Ks likely V E ± 0.18 mag, P= hr J V C ± 0.8 mmag, P= 2 ± 0.4hr JHKs C KTTK05 J < 15 mmag, H < 11 mmag, K < 2 mmag 8.46 GHz C B06 < 42µJy 2MASS J HST G141 grism V Bu13 Ic C K13 Ks C E03 < 7% J C08 C < 5 mmag Ic C K GHz B06 < 27µJy 2MASS J HST G141 grism V Bu13 DENIS J HST G141 grism V Bu13 2MASS J K V Kh mag J C < mag 2MASS J Ic C K13 Ic C K05 JHKs C KTTK05 J < 10 mmag, H < 11 mmag, K <18 mmag JHKs V KMM04 H 4 mmag, K 7 mmag, P= 0.96 hr 8.46 GHz C B06 < 63µJy 2MASS J HST G141 grism V Bu13 Variability detected in water band ( µm) JHKs C KMM GHz C B06 <36µJy 2MASS J J V C08 J = 12.4 ± 1.3 mmag, P=2.9±0.9 hr Objects with reported Optical variability measured as constants in this study 2MASS J Ic V K13 References: Artigau et al. (2003) [A03], Artigau et al. (2009) [A09], Apai et al. (2013) [Ap13], Berger (2006) [B06], Buenzli et al. (2012) [Bu12], Buenzli et al. (2013) [Bu13], Clarke et al. (2008) [C08], Enoch et al. (2003) [E03], Gelino et al. (2002) [G02], Khandrika et al. (2013) [Kh13], Koen (2004) [K04], Koen et al. (2004) [KMM04], Koen et al. (2005) [KTTK05], Koen (2005) [K05], Koen (2013) [K13], Radigan et al. (2012) [R12], Zapatero Osorio et al. (2006) [Z06]

126 Weather in the atmospheres of Brown Dwarfs 100 Table 3.6: Summary of constant sources. Target Name Band References Notes 2MASS J I c K13 2MASS J JK Kh13 no results 2MASS J GHz B06 < µjy 2MASS J I c K13 I c K GHz B06 < 66µJy 2MASS J I c K13 I c K GHz B ± 14µJy 2MASS J J KTTK05 < 12 mmag H < 14 mmag K s < 9 mmag JHK s KMM04 2MASS J I c K GHz B06 < 87µJy 2MASS J JHK s KMM04 J Gi13 < 5mmag 2MASS J I c K13 I c K GHz B06 < 57µJy 2MASS J J Kh13 < 3.3% K < 6.1% 2MASS J JHK s KMM04 2MASS J JHK s KMM04 2MASS J GHz B06 < 54µJy HST G141 Grism Bu13 2MASS J I c K13 2MASS J I c K13 References: Berger (2006) [B06], Buenzli et al. (2013) [Bu13], Girardin et al. (2013) [Gi13], Khandrika et al. (2013) [Kh13], Koen (2004) [K04], Koen (2003) [K03], Koen et al. (2004) [KMM04], Koen et al. (2005) [KTTK05], Koen (2005) [K05], Koen (2013) [K13]. To calculate the uncertainty on the variability frequency we use the binomial distribution B(n; N, ɛ v ) = N! n!(n n)! ɛn v (1 ɛ v ) N n. (3.3) Detection probability for the sample (%) Amplitude (%) Figure 3.8: Proportion of the survey sensitive to variability as a function of peak-to-trough amplitudes for different detection thresholds. The dashed line represents the fraction of objects with a photometric accuracy good enough to have allowed for the detection of variability. The shaded area represents the region of sensitivity with the upper binomial errors and amplitude uncertainties added to the variability fraction.

127 Weather in the atmospheres of Brown Dwarfs Variability Frequency (%) Amplitude (%) Figure 3.9: Variability frequency as a function of amplitude (dashed line) with the binomial errors and amplitude uncertainties added to the variability fraction (shaded area). Variable Detection Probability (%) Amp = 1.5% Amp = 2.5% Amp = 5.0% Period (hours) Figure 3.10: Percentage of simulated sinusoidal light curves detected as variable, as a function of period from 1 hour to 12 hours, for three different amplitudes. We used the measured survey median noise of 0.7%, and each sine curve was sampled at intervals of 15 minutes to imitate the binned data of the survey. Additionally, we stepped through each sine curve at 5 degree phase intervals, to ensure that we sampled the full phase of the variable light curve.

128 Weather in the atmospheres of Brown Dwarfs 102 where n is the number of variables, N the sample size and ɛ v the variability frequency. This approach is based on Bayes theorem under the assumption of a uniform prior based on no a priori knowledge and is ideal for small samples such as is the case for the BAM survey. The rotation period is another factor that can influence the detectability of a variable signal. In Figure 3.10, we present the results of simulating light curves to test the detection probability of the survey to brown dwarf variables with different periods. We simulated sinusoidal light curves with three different amplitudes, of 1.5%, 2.5%, and 5.0%, and with periods ranging from a minimum of 1 hour to a maximum of 12 hours (Zapatero Osorio et al. 2006). Gaussian noise equal to the median photometric uncertainty of the survey of 0.7% was added to each light curve. To mimic the binned SofI data, the light curves were sampled at intervals of 15 minutes, and each simulated dataset was divided into groups of 3 hours, similar to the typical duration of the BAM data. For light curves with period longer than 3 hours, we generated multiple datasets, by stepping through the sine curve in steps of 5 degrees of phase and calculating the p-value at each phase, ensuring full sampling of the phase. Figure 3.10 shows the percentage of simulated light curves that are detected as variable with a p-value 5%. For amplitudes of 5.0%, periodicities from 3 to 12 hours are easily recovered with a probability of 80 to 100%, while the required periods decrease to 6 hours for 2.5% variables and 5 hours for 1.5% variables for detection probabilities in the 80 to 100% range Frequency and amplitude of variability across spectral types The frequency of variables as a function of spectral type is an important topic, since models of brown dwarf atmospheres have suggested that breakup of clouds across the L/T transition may result in both a higher rate of occurrence and a higher amplitude of variability compared to earlier L and later T objects. Amongst the previously known variables, the two largest amplitude variable objects discovered to-date are L/T transition objects - SIMP0136 ( 5% in J-band but with a significant night to night evolution, Artigau et al. 2009) and 2M2139 (as high as 26% in the J-band, Radigan et al. 2012). As indicated by the variability frequencies reported in Table 3.7, the BAM results show no evidence that the frequency of variables in the L7 to T4 transition region is distinct from the earlier spectral types, the later spectral types, or the combination

129 Weather in the atmospheres of Brown Dwarfs 103 Table 3.7: Variability frequency. Sample Sp. Type No. Targets No. Variables Freq. (%) Early-L L0-L Late-T T5-T L/T Transition L7-T Outside L/T transition L0-L6 & T5-T Notes: These are the variables with a p-value 5%, and amplitude 2.3%. σ (mmag) Temperature Range (K) < > L0 L2 L4 L6 L8 T0 T2 T4 T6 T8 Spectral Type σ(%) (J-K) 2MASS (mag) L0 L2 L4 L6 L8 T0 T2 T4 T6 T8 Spectral Type Figure 3.11: Diagram on the left shows the amplitude of the variables (pvalue 5% closed circles and 5% < p-value 10% closed circles with cross) as well as the target photometric uncertainty of the non-varying objects (coloured triangles) across the entire spectral range of the sample. The diagram on the right shows the colour-colour diagram of the entire L through T spectral range with the full sample plotted with open circles, showing the colour spread of the targets. The variables from the BAM sample are overplotted (p-value 5% closed circles and 5% < p-value 10% closed circles with cross). The L/T transition is indicated by the dashed lines of all non-transition region brown dwarfs. The variability frequencies in Table 3.7 are calculated using the entire sample of targets and an amplitude threshold of 2.3% and p Although no statistically significant difference in the variability frequencies for transition brown dwarfs is measured with the BAM survey, the 2.3% amplitude limit of the analysis would not have detected differences at lower amplitudes, and removing the peak-to-trough amplitude threshold does not change this result. Adjusting the boundaries of the transition region by up to two spectral types does not change the result. Likewise, the amplitudes of the detected variables show no clear trends with spectral type within the capacity of the survey, as shown in Figure 3.11 (left). The measured amplitude is sensitive to deviant photometric measurements which have the effect of possibly overestimating the measured amplitude (i.e. last point in 2M1300). Identifying a minimum upper limit and a maximum lower limit could avoid such a bias for some of the

130 Weather in the atmospheres of Brown Dwarfs 104 light curves. However, for light curves showing multi-component variability it is not clear which photometric points would be best suited for the amplitude calculations (i.e. 2M1126). Light curves showing deviant points where visually inspected to insure no cosmic rays affected the data. Not accounting for variables which are identified as variables due to one or two possibly deviant photometric points does not introduce a change in variability frequency amongst the earlier, transition or later spectral types. In the interest of keeping the amplitude determination uniform throughout the sample, and to remove any human bias introduced in selecting upper and lower amplitude limits, the max-min amplitude is calculated using all the points in the light curve. The BAM variability frequency is very comparable to estimates for M stars. A variability frequency between 21 29% for 19 M-stars was measured in a multiwavelength optical study with the Calar Alto Observatory in Spain (Rockenfeller et al. 2006). The wavelength of observations for the M-star study was shorter than the BAM survey J-band data, and the amplitude of variations is expected to decline for longer wavelengths (e.g. Reiners et al. 2010). In a recent compilation of variability surveys, Khandrika et al. (2013) reported a variability frequency of 30 ± 5% based on a collection of different surveys with observations obtained in the optical and near-ir passbands, covering 78 objects in total. Comparison between surveys is difficult as the variability frequency may depend on a variety of different factors, including the target selection criterion and the criteria used to define variability in the targets which usually differs from one survey to the next. Additionally, the observed wavelength may also alter the variability frequency with different wavelength probing different depths in the atmosphere. Koen (2013) finds a poor overlap between the variables identified with optical and near-ir filters (of the 13 variables already observed in near-ir surveys, 7 were found as constant and 6 as variable in the optical). Because of the uniform sensitivity of this survey, we did not incorporate the results of previous studies into the statistics, presented in Table 3.7. The presence of highly variable objects outside the transition region, may suggest the possibility of both early onset of cloud condensation in the atmospheres of mid-l dwarfs and the emergence of sulfide clouds in mid-t dwarfs (Morley et al. 2012). The contribution of magnetic fields to the observed variabilty, especially for early L-type objects, is still an open question althogh most brown dwarfs are likely too cool to exhibit magnetic spots (Gelino et al. 2002; Mohanty et al. 2002). Other physical processes that have been

131 Weather in the atmospheres of Brown Dwarfs 105 suggested to possibly induce variability in the atmospheres of brown dwarfs include coupling clouds with global atmosphere circulation (Showman & Kaspi 2013; Zhang & Showman 2014), and variability caused by thermal perturbations emitted from deeper layers within the brown dwarf atmosphere (Robinson & Marley 2014) Variability as a function of colour within a spectral type The J K colour of the sample as a function of the spectral type is shown in Figure The targets span nearly the full colour spread of early-l, transition and late-t sub samples. The 14 BAM variables and the three candidates are not clustered toward either the red or the blue within any particular spectral type. Previous studies (e.g. Khandrika et al. 2013) have suggested that brown dwarfs with unusual colours (highly red or blue) compared to the median of the spectral type might be indicative of variable cloud cover. We performed a two sample K-S test to determine whether or not the detrended colors of the BAM variables were distinct from the rest of the sample. The maximum difference between the cumulative distributions was 0.18 with a corresponding p-value of 75%, indicating that the two datasets are consistent with being drawn from the same sample. The BAM study thus finds no correlation between the variables and the colour of a brown dwarf within each spectral type Binarity and variability The BAM sample includes 12 confirmed binaries out of 47 targets studied for binarity with another four SpeX spectra binary candidates. Including the binary candidates, 10 out of the 16 binaries in the BAM sample fall in the L/T transition. This is consistent with previous detections of an increase in the binary frequency across the L-T transition Burgasser et al. (2006). Amongst the BAM variables, only 2M2255 is a confirmed binary, while 2M1207 and 2M2139 are binary candidates. Amongst the non-variable objects no correlation between non-variability and binarity is observed in the L/T transition. A BD binary system can mimic a L/T transition BD if the combined light from the unresolved binary system originates from a pair of BDs which individually may not have a spectral type within the L/T transition. To investigate if such an effect would alter the results we calculate the variability frequency of objects confirmed to be single within each of the

132 Weather in the atmospheres of Brown Dwarfs 106 spectral bins. We find the measured frequency of the L/T transition to be indistinguishable from the earlier and later spectral types. The limited data provides no evidence to support a correlation between variability and binarity amongst the objects in the BAM survey Persistence of variability A recent multi-epoch ( 4 years) monitoring study of the variable brown dwarf SIMP0136 (Metchev et al. 2013) revealed that the target has significant evolution in its light curve, changing from highly variable to constant in a 2 month period. When compared to the SofI light curve for SIMP0136, the target shows a fascinating variation in amplitude. It appears to be variable at 3% in the SofI data, while a month later it shows large amplitude variations ( 9%) in the J-band, only to appear constant a few months later. Similar night-to-night variations have also been seen in SDSS J (Girardin et al. 2013). The evolution indicates a lack of persistence in the source of variability over timescales longer than a few weeks and it suggests that the brown dwarfs identified as constant in this study might similarly exhibit periods of quiescence and enhanced activity. The BAM survey only examines variability on the timescale of a single rotation period or less as compared to some surveys (e.g. Enoch et al. 2003; Gelino et al. 2002) that study the flux variations of brown dwarfs over longer timescales. The BAM data, in combination with previous results, can be used to address the question of persistence of variability. Table 3.8 summarizes the observations related to persistence of variability, using information presented in Table 3.5 and 3.6. For greatest consistency with the BAM study, we consider other epochs of near-ir data rather than optical. A total of 34 BAM targets have an earlier epoch of observation. 2M0228 is the only source measured to be variable in the optical (I c ) that switched from variable to constant. Table 3.8 indicates that brown dwarf variability does not necessarily persist on longer timescales, with only half the BAM variables showing variation in both epochs. The survey finds four previously constant objects to be variable and nine targets previously reported as variable in the literature to be constant, making these ideal candidates for multiple epoch monitoring programs.

133 Weather in the atmospheres of Brown Dwarfs Summary Table 3.8: Summary of Persistence Results Total targets with 2 epochs 34 Variable at 2 epochs 6 Constant at 2 epochs 15 Switch between variable and constant 13 We present the results of the largest near-ir brown dwarf variability survey conducted in the J s -band using the NTT 3.5 m telescope. The BAM survey has an unbiased sample of 69 early-l through late-t brown dwarfs. A total of 14 variable objects were detected: six new variables not previously studied for variability, three objects previously reported as constant, and five previously known variables. The nine newly identified variables constitute a significant increase in the total number of known brown dwarf variables characterisable using ground-based facilities. In a recent study of 57 L4-T9 brown dwarfs (Radigan et al. 2014), a set of 35 targets were observed by both studies, enabling a direct comparison of results. Of the 35 targets in both samples, both studies classify a common 26 targets as not variable and a common 4 targets as variable. Of the 5 remaining variables noted in a single study (2 in BAM, 3 in Radigan et al. 2014), 4 can be explained by differences in sensitivity for the specific light curves. Rather than quoting a single number for the variability frequency, we discuss how the frequency of variable brown dwarfs depends on different factors such as the observed wavelength and the variability amplitude. The BAM study, representing the largest and most uniform ground-based search for variability, was designed to address the important question of the physical properties of brown dwarf atmospheres including the L-T transition. One class of models has suggested that this colour change, that defines the transition, may be a manifestation of the breakup of clouds resulting in a patchy coverage across the surface (Ackerman & Marley 2001), which would have the observable consequence of enhanced variability at the L-T transition. Considering the results of this study, covering both transition and non-transition objects and statistical significance of the variability, there is no distinction between the variability frequency between the brown dwarfs in the transition region or outside the transition region. This suggests that the patchy cloud scenario may not provide the full explanation for the L-T transition or that the induced level of variability is substantially below the detection thresholds of

134 Weather in the atmospheres of Brown Dwarfs 108 the current study. The 14 variables, including the nine newly identified variables, will provide valuable systems with which to pursue additional questions of the physics of brown dwarf atmospheres, including the longitudinal and vertical variations of clouds and active regions which can be inferred from multi-wavelength follow-up monitoring. Acknowledgements: Based on observations made with ESO Telescopes at the La Silla Paranal Observatory under programme ID 188.C We would like to thank the anonymous referee for valuable suggestions thats helped improve this paper. PAW acknowledges support from STFC. JP was supported by a Leverhulme research project grant (F/00144/BJ), and funding from an STFC standard grant. This research has made use of the SIMBAD database and VizieR catalogue access tool, CDS, Strasbourg, France. The original description of the VizieR service was published in A&AS 143, 23. This research has benefitted from the M, L, T, and Y dwarf compendium housed at DwarfArchives.org. This research made use of Astropy, a community-developed core Python package for Astronomy (Astropy Collaboration et al. 2013). We thank F. Pont, R. De Rosa and D. K. Sing for valuable feedback and discussion. 3.3 Developments since publication Subsequently with the publication of Wilson et al. (2014) a paper addressing many of the same questions was published by Radigan et al. (2014) who studied variability in 57 L4-T9 brown dwarfs. The main difference between the studies, in terms of scientific results, is that Radigan et al. (2014) find J-band variability of BD with peak to peak amplitudes 2% to be rare outside of the L9-T3.5 spectral range whereas Wilson et al. (2014) find high amplitude variables to be more evenly distributed amongst the brown dwarf spectral classes. The reason behind the different conclusions is not yet clear and could be due to the methods used in determining variability or the initial sample or a combination of both. Although every effort was made to minimize systematics in Wilson et al. (2014), there is still a chance that unaccounted for systematics could remain in the data which mimic real variability. These false variables should be contained within the

135 Weather in the atmospheres of Brown Dwarfs false positives which exist in the data (as inferred from the p-value determination). The survey sample in Radigan et al. (2014) is distinctly lacking in number of L-type objects, with the L-type objects being biassed towards bluer colours compared to most L-dwarfs. Partial cloud cover may explain the bluer L-dwarfs and as such the L-dwarf sample may be biassed towards objects which more likely show variability. The deficiency of unbiased L-dwarfs could be complimented by studies by Koen et al. (2004) and Clarke et al. (2008) who both find no evidence for J-band variability above a peak-to-peak amplitude of 2%. However, these studies use different variability criteria. The approach by Radigan et al. (2014) assumed the variability to be strictly sinusoidal in nature and does not account for objects with more erratic variations. The two studies also share many similarities. Amongst the 35 objects common to both studies, 86% of them were both consistent in their classification typing an object as either non-variable or variable. For the remaining five variables, which differ between the two studies, four of them can be explained by differences in sensitivity. In terms of detected variability as a function of spectral type, the surveys are very similar, as can be seen in Fig and Fig as well as Table 3.9 and Table 3.10.

136 Weather in the atmospheres of Brown Dwarfs Targets 23 Targets 23 Targets 8 BD Number L0 L2 L4 L6 L8 T0 T2 T4 T6 T8 Y0 Spectral Type Figure 3.12: Histogram of the BAM sample across their respective spectral classes. The sample size is represented by the gray histograms whilst the variables are coloured Targets 28 Targets 20 Targets 8 BD Number L0 L2 L4 L6 L8 T0 T2 T4 T6 T8 Y0 Spectral Type Figure 3.13: Histogram of the Radigan et al. (2014) sample across their respective spectral classes. The sample size is represented by the grey histograms whilst the variables are coloured. The hatched areas symbolise the marginal detections at > 96% confidence.

137 Weather in the atmospheres of Brown Dwarfs 111 Table 3.9: Variability frequency from Wilson et al. (2014). Sample Sp. Type No. Targets No. Variables Freq. (%) Early-L L0-L Late-T T5-T L/T Transition L7-T Outside L/T transition L0-L6 & T5-T Notes: These are the variables with a p-value 5%, and amplitude 2.3%. Table 3.10: Variability frequency from Radigan et al. (2014). Sample Sp. Type No. Targets No. Variables Freq. (%) > 96% > 99% > 96% > 99% Early-L L0-L Late-T T5-T L/T Transition L7-T Outside L/T transition L0-L6 & T5-T Notes: Significant detections: > 99% confidence, Marginal detections: > 96% confidence.

138 Weather in the atmospheres of Brown Dwarfs M Sim. Ref Relative Flux Time (hr) Figure 3.14: 2M observations with the NOT (red) shown together with a similar brightness reference star (blue). Data discarded from the analysis is marked in grey. A simple best-fit sine curve gives a peak-to-peak amplitude of 2.0 % and a period 4 hours Follow-up observations at the NOT and NTT After the initial submission of BAM survey paper, observations of 2MASS J were conducted at the Nordic Optical Telescope (NOT) program P (PI: Wilson, P. A.), using a similar bandpass filter, aimed at confirming the variability. The resulting light curve from the NOT observations are shown in Fig A simple sine curve was fit to the NOT data using a modified Levenberg-Marquardt algorithm which gave an estimate of the period 4 hours and peak to peak amplitude of 2.0 %. The uncertainties where checked against the standard deviation of the similar brightness reference star. The χ 2 red of the sine fit gives 0.4 compared to a straight line which gives 5.0. No correlation with FWHM is observed. The data from the BAM survey was revisited and the photometry performed again, this time specifically optimising the 2M observations by selecting the most optimal aperture for this object. The resulting unbinned light curve is shown in Fig A sine fit to this data gives a matching period of 4 hours however with a larger peak to peak amplitude of 4.7%. During the analysis a seeing variation was observed which showed similar variations to the 2M light curve. None of the reference stars showed this variation so it is uncertain to what degree it may have affected the light curve, especially the amplitude. As both observations

139 Weather in the atmospheres of Brown Dwarfs Relative Flux Time (hr) Figure 3.15: 2M observations with the NTT (red) shown together with a similar brightness reference star (blue). Data discarded from the analysis is marked in grey (poor seeing). A simple best-fit sine curve gives a peak-to-peak amplitude of 4.7 % and a period 4 hours. acquired on different nights using different telescopes show similar periods, it is highly likely that the period is real in both cases. Follow-up observations of the variable BAM survey targets are currently underway at the NTT telescope. The observations will allow for the confirmation of the variables and allow their variability to be characterised as a function of time and atmospheric depth using multi wavelength observations. The contamination due to unresolved binaries, can be reduced by searching for binarity amongst the objects in the BAM survey. This can be done by looking for RV variations in the BD spectra. Obtaining low resolution spectra and comparing these spectra to synthetic models, spectral LT binaries can be identified. Parallax measruements would allow likely binaries to be flagged if the object appears brigther than is expected for a single object in the CMD.

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141 Chapter 4 The Atmospheres of Exoplanets 4.1 Detection of potassium in HAT-P-1b from narrowband spectrophotometry Disclaimer The work below is not published and may be subject to slight change. The paper below will be published in the Monthly Notices of the Royal Astronomical Society Abstract We present the detection of potassium in the atmosphere of HAT-P-1b using optical transit narrowband photometry. The results are obtained using the 10.4-m Gran Telescopio Canarias (GTC) together with the OSIRIS instrument in tunable filter imaging mode. We observed a total of three transits, one outside the potassium feature at Å (R=566) and two probing the potassium feature by alternating the observed wavelengths between the line wing at Å (R=632) and the line core at Å (R=639). The planet-to-star radius ratios are found to be R pl /R = ± for Å, R pl /R = ± for Å and R pl /R = ± for Å using a 12 Å filter width. Compared to the weighted means of previous HST observations centred at Å and Å, the detection of potassium is evident from an increase in the radius ratio of ± at Å (6.7 σ significance) and 115

142 The Atmospheres of Exoplanets 116 R pl /R = ± at Å (10.1 σ significance). Fitting a potassium profile to our data we derive a temperature of 1332 ± 407 K. We hypothesize that the strong detection of potassium is caused by a large scale height, which can be explained by a higher than anticipated temperature in the upper atmosphere, or by the dissociation of molecular hydrogen into atomic hydrogen caused by the UV flux from the host star. We note that high resolution observations are essential for detecting very narrow alkaline spectral features such as those seen in HAT-P-1b and HD b Introduction Transiting exoplanets provide us with a unique opportunity to study the structure and composition of their atmospheres. A valuable insight into the planet s atmosphere is gained by measuring the amount of stellar light which passes through the exoplanet atmosphere as a function of wavelength. The amount of light obscured by the transiting exoplanet is dependent on the atmospheric composition of its atmosphere, with absorbing species letting less light through at specific wavelengths, leading to a change in the exoplanet radius as a function of wavelengths. For hot Jupiters which are not dominated by clouds and hazes, the two most dominant sources of opacity in the optical are thought to be the alkali metals sodium and potassium (Seager & Sasselov 2000), with their resonance doublets at 5890, 5896 Å and 7665, 7699 Å respectively. Sodium was first detected by Charbonneau et al. (2002) in the atmosphere of HD b using the Space Telescope Imaging Spectrograph (STIS) on the Hubble Space Telescope (HST). These observations were later confirmed by Snellen et al. (2008) using the High Dispersion Spectrograph at the Subaru telescope. Exoplanetary sodium has also been found to be present in the atmospheres of HD b (Huitson et al. 2012; Redfield et al. 2008), XO- 2b (Sing et al. 2012) and WASP-17b (Wood et al. 2011; Zhou & Bayliss 2012). Exoplanetary potassium has been detected on the hot Jupiters XO-2b (Sing et al. 2011b) and HD 80606b (Colón et al. 2010) who, similar to this work, used tunable filters (TFs) with the Optical System for Imaging and low Resolution Integrated Spectroscopy (OSIRIS) instrument at the Gran Telescopio Canarias (GTC). TFs have the unique capability of allowing the central wavelength and filter passband tuned to a specific value. The TF consists of a Fabry-Pérot etalon made up of two parallel reflective surfaces. By varying the separation between the two plates,

143 The Atmospheres of Exoplanets 117 the filter width and central wavelength can be chosen. TF have several advantages over low resolution spectroscopy. They provide accurate differential photometry whilst also allowing for relatively high resolution measurements (R ), compared to a low-resolution grism on OSIRIS (R ). TFs have the unique advantage that they can be tuned to a wavelength not contaminated by strong telluric lines such as the prominent O 2 lines at 6884 and 7621 Å (Catanzaro 1997). Since no diffraction gratings are used, TFs can be much more efficient (Colón et al. 2010), especially for observing atomic absorption features which typically have a narrow spectral range. Combining this technique with the 10.4 m aperture of the GTC telescope makes it possible to study the atmospheres of planets orbiting stars fainter than HD and HD , which due to apparent brightness, and large atmospheric scale heights, are the two best studied cases thus far. In this study we present the detection of potassium in HAT-P-1b (Bakos et al. 2007), a R Jup exoplanet with a mass of M Jup and thus a low average density of ρ = g/cm 3 on a 4.47 day circular orbit around a G0V star at a distance of AU (Bakos et al. 2007; Johnson et al. 2008). The host star appears to not be very active (Knutson et al. 2010) with HAT-P-1b showing signs of a modest temperature inversion layer (Todorov et al. 2010). With its low density and large radius HAT-P-1b is an interesting test case for interior and atmosphere models. These observations are a part of our larger spectrophotometric survey aimed at detecting and comparing atmospheric features in transiting hot Jupiters (ESO programme 182.C-2018). In this paper we present our results on TF observations of HAT-P-1b with the GTC telescope. In we describe the observations, and in we describe the analysis of the transit light curves. In we present a discussion of the results were we compare the observations to a model atmosphere, and conclude in Observations Observations were performed using the 10.4 m GTC telescope located at Observatorio del Roque de los Muchachos of the Instituto de Astrofísica de Canarias on

144 The Atmospheres of Exoplanets 118 the island of La Palma. Narrowband imaging was done with the OSIRIS instrument using the red tuneable filter (operating range of 6510 Å Å) tuned to the minimum width of 12 Å Instrumental setup The OSIRIS instrument (Cepa 1998; Cepa et al. 2000, 2003) consists of a mosaic of two Marconi CCD42-82 CCDs each with a 2048 x 4096 pixel detector separated by a 72 pixel gap between them. Each pixel has a physical size of 15 µm, which gives a plate scale of The observations were performed without any binning with a readout frequency of 500 khz and a gain of 1.46 e / ADU on CCD2. This setup gives a readout noise of 8e. The observations tuned to Å were performed using the whole CCD2 array. Being one of the first OSIRIS observations, a subarray mode was not offered. Later observations have since been performed in the sub-array mode as it reduces the read time yielding a higher cadence, and because the photometry of the first observations was not improved by including other fainter stars in the HAT-P-1 field. The observations tuned to and Å were windowed to pixels. To obtain the highest possible resolution the smallest possible passband of 12 Å was chosen Observing log HAT-P-1b was observed on three separate nights. For all observations, the companion star HAT-P-1-B (BD p) was used for photometric comparison, and its close 11 proximity allowed for windowed frames to be taken. The frames were also rotated to ensure that both the target and the comparison star were at the same radial distance from the centre of the CCD, ensuring that both objects were observed at the same wavelength. 22 October 2009: The tunable filters where centred on the continuum at Å. The observations began at 20:42 UT, about 15 min later than planned, due to issues with the OSIRIS setup, and ended at 02:25 UT. Due to variable seeing, ranging from about 1.4 to 0.7 arc seconds, the exposure time was frequently adjusted to avoid saturation. Being the first observations with the OSIRIS instrument in our program there were still issues present concerning the dark current. Hardware upgrades have since solved the issue.

145 The Atmospheres of Exoplanets November 2010: The tunable filters where centred at Å and Å, resulting in near simultaneous light curves at two wavelengths sampling the line wing of the potassium feature and the core of the KI D2-line. The observations started late at 22:15 UT due to high humidity and ended at 01:29 UT. Seeing was variable ranging from 0.8 to 1.3 arc seconds. The exposure was adjusted to avoid saturation. An hour into the observations light cirrus clouds were present. 26 November 2013: These observations were a repeat of the 19 November 2010 observations and used the same setup. To decrease the overheads the exposure times were increased. Observations started late at 22:16 (due to high humidity) and ended at 01:29 UT (lower elevation limit of the GTC of 25 degrees) Reductions The image reductions were made by combining the bias frames and sky flats using standard IRAF 1 routines. Dark frames were only obtained for observations at Å as the issue with high dark current noise was corrected in time for the subsequent observations. Due to the short exposure times, the dark frames did not improve the reduction and where therefore not used. Aperture photometry was done using the APPHOT package in IRAF. In order to ensure the best possible photometry, a large range of apertures were explored varying both the aperture size as well as the dimensions of the sky annuls in order to minimise the scatter of data points in the continuum. The differential photometry was performed with the target and the nearby reference star at the same wavelength. The resulting light curves are shown in Fig. 4.1 and Fig Analysis Light curve fits The transit light curves were generated using only one reference star and were fitted using the analytical transit equations of Mandel & Agol (2002). The best fitting parameters together with their associated uncertainties were determined 1 IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation.

146 The Atmospheres of Exoplanets 120 by a Markov chain Monte Carlo algorithm (MCMC) in the same way as (Wilson et al. 2014). The initial starting parameters were from Nikolov et al. (2014). Time dependent correlations with airmass, FWHM and detector position were, when significant enough as determined by the Bayesian Information Criterion (BIC), used to model the systematics in the data. No sky-rings are seen in the data making it impossible to measure a possible wavelength shift. All the transits had the radius ratio, R p /R s, central transit time T C, a baseline normalising factor, N and a slope term s as free parameters. The Å light curve was fit with an additional linear FWHM term (time FWHM+1). The half transits observed at Å and Å on 19 November 2010 showed no detectable systematic noise leading to no additional free parameters. The full transit observations conducted on 26 November 2013 were fit with both a linear FWHM term (time FWHM+1) and a quadratic airmass term (time airmass 2 +1). The fixed parameters were the period, P = ±(55) days, impact parameter b = and the quadratic limb-darkening coefficients, u 1 and u 2, which were calculated using the ATLAS stellar atmospheric models 2 following Sing (2010). A quadratic limb darkening law of the following form was used I(µ) I(1) = 1 u 1(1 µ) u 2 (1 µ) 2, (4.1) where I(1) is the intensity at the centre of the stellar disk, µ = cos(θ) is the angle between the line of sight and the emergent intensity while u 1 and u 2 are the limb darkening coefficients. The stellar and orbital parameters were also kept fixed with R s = R, the eccentricity e = 0 and the scaled semi-major axis a/r s =

147 The Atmospheres of Exoplanets 121 Norm. Raw Flux Normalized Flux O-C ( 10 3 ) Orbital Phase Figure 4.1: The Å observations (outside the potassium feature) with the raw light curve shown in the top panel, the corrected light curve in the middle panel and the best fit residuals shown in the bottom panel.

148 The Atmospheres of Exoplanets 122 Norm. Raw Flux Normalized Flux O-C ( 10 3 ) Orbital Phase Figure 4.2: Light curves probing the potassium feature. The first and third columns (yellow points) corresponding to observations at Å, and the second and fourth column (red points) corresponding to the core of the potassium line at Å. The half transits were obtained 19 November 2010 whilst the full transits were obtained on 26 November 2013.

149 The Atmospheres of Exoplanets 123 Table 4.1: Light curve system parameters for HAT-P-1b Parameter Å Å Å Å Å T0 [BJD] (33) (26) (29) (30) (27) Rpl/R ± ± ± ± ± u u σw σr Half transits

150 The Atmospheres of Exoplanets Noise Estimate Following the procedures of Carter & Winn (2009b) the wavelet method was used to calculate the uncorrelated noise term, σ w, and the systematic noise term, σ r. Using these terms a β-factor expressed as β = 1 + ( σr σ w ) 2 (4.2) was computed and used to used to incorporate the effects of systematics noise in the calculations of the uncertainties on the radius ratio. The transits are all dominated by white noise indicating the the light curves are largely affected by photon noise Results and Discussion The detection of potassium We observed three transits, one of which was outside the potassium feature at Å (R=566) and two inside the potassium feature probing the line wing at Å (R=632) and the line peak at Å (R=639). Both the raw and detrended light curves together with their best fit light curve models are shown in Fig. 4.1 and Fig. 4.2 with their best fit model parameters shown in Table 4.1. A transmission spectrum of HAT-P-1b showing results form this study as well as Nikolov et al. (2014) and Wakeford et al. (2013) are shown in Fig Compared to the weighted means of previous HST observations centred at Å and Å, the detection of potassium is evident from an increase in the radius ratio of R pl /R = ± at Å (6.7 σ significance) and R pl /R = ± at Å (10.1 σ significance) The effects of temperature To assess possible scenarios for the large atmospheric scale height inferred from the observations, we explore the possibility of a temperature inversion in the upper atmosphere. We model the potassium D doublet and fit it to the potassium

151 The Atmospheres of Exoplanets Rp/R Wavelength [Å] Figure 4.3: Transmission spectrum of HAT-P-1b. The data is from Nikolov et al. (2014) (red and blue points at optical wavelengths), Wakeford et al. (2013) (purple points at near-ir wavelengths) and Wilson et al. (2014) (hexagonal points). The model transmission spectra assume an isothermal hydrostatic uniform abundance with a equilibrium temperature of 1200 K. The magenta line is an isothermal model by Burrows et al. (2010) with an extra absorber at altitude with an opacity of 0.03 cm 2 g 1 from 0.4 to 1.0 µm. The brown line is a 1200 K isothermal model (without TiO/VO) by Fortney et al. (2008, 2010). probing observations at Å and Å. At the wavelengths and pressures probed, the potassium profile is dominated by natural broadening with pressure broadening providing a negligible contribution. For our calculations, we assume potassium is the dominant opacity source at the wavelengths probed. Extracting a temperature from the potassium profile also assumes an isothermal atmosphere with a constant gravity and a mean molecular weight which does not change with altitude, a valid assumption for local measurements. The cross section profiles for each data point therefore depends on the local temperature, but does not depend on the reference pressure, abundances, gravity or the mean molecular weight. We calculate the absorption cross sections for the potassium probing wavelengths by convolving the potassium absorption cross section profile with the GTC tunable filter (TF) response curves. The spectral transmission of a TF is expressed as: { [ ] } 2 1 2(λ λ0 ) T = 1 + (4.3) δλ

152 The Atmospheres of Exoplanets 126 where λ 0 is the wavelength at maximum transmission and δλ the passband width 3. Given an atmospheric structure and composition, the effective altitude as a function of wavelength, can be calculated using the following relation: ( ) z(λ) = H ln ξ abs P z=0 σ abs (λ)/τ eq 2πR p /kt µg (4.4) described in detail in Lecavelier Des Etangs et al. (2008). In the equation above ξ abs is the abundance, σ abs the cross section, τ eq the optical depth, R p the radius of the planet, k the Boltzmann constant, T the temperature, µ the mean molecular weight, g the gravity and H the scale height H = kt/µg. Using Eq. 4.4 the planet-to-star radius ratio values for the two potassium probing wavelengths are calculated using the previously calculated absorption coefficients. We measure the local temperature by performing a MCMC analysis with temperature and a vertical shift of the transmission spectrum as free parameters. The shift is dependent on the abundance of potassium and the reference pressure at the reference zero altitude, which we are not able to constrain independently. For our calculations we assume a solar potassium abundance and a mean molecular weight of 2.35 m u. We derive a temperature of T = 1332 ± 407 K for our isothermal potassium model and shown with the convolved potassium profile binned into 12 Å bins in Fig The apparent slope seen towards shorter wavelengths in the data of Nikolov et al. (2014) could be due to Rayleigh scattering. As the composition of the gases which might affect this slope is not well known, we derive a temperature assuming a Rayleigh slope only described by molecular hydrogen, the most abundant molecule. We calculate the best fitting temperature inferred from the Rayleigh slope to be K. The best fit slope with associated uncertainties is shown in Fig The temperatures derived using the above methods are primarily limited by the lack of data points and can thus only provide loose constraints on the temperature. Using Spitzer/IRAC secondary eclipse photometry Todorov et al. (2010) derived an average dayside temperature of 1500 ± 100 K. Wakeford et al. (2013) find a 1000 K isothermal model by (Fortney et al. 2008, 2010) best fit the water feature detected in the planet, whereas Nikolov et al. (2014) find a 1200 K isothermal model best represents the data. The data presented here are consistent with the above previous results. 3 see OSIRIS User Manual v3.1

153 The Atmospheres of Exoplanets Rp/R Wavelength [Å] Figure 4.4: Best fit potassium line profile to the GTC observations at Å and Å (hexagonals). The potassium profile has been binned by convolving the potassium profile with the TF transmission curve. The wavelength bin sizes are indicated by the width of the symbols with the vertical error bars representing the 1σ uncertainties. The best fit potassium line is that a of a T = 1332 ± 407 K model. The 1σ uncertainties in the fit are represented by the shaded regions. The enhanced absorption measured at the potassium probing wavelengths compared to previous HST data (Nikolov et al. 2014) could be due to a larger temperature at the layers where the potassium is being probed. The result could be indicative of a thermosphere as the core of the potassium line probes higher regions in the atmosphere (typically 10 3 to 10 6 bars), where a large increase in temperature is not uncommon in solar system planets (Lindal et al. 1985, 1981). This transition region between the lower atmosphere and the outermost, hottest layers of the upper atmosphere is referred to as the base of the thermosphere. High upper atmospheric temperatures are particularly relevant to hot-jupiter planets as predicted by models (e.g., García Muñoz 2007; Tian et al. 2005; Yelle 2004) The effects of potassium abundance and mean molecular weight The observed radius ratio increase could in part be due to an enhanced abundance of potassium high in the atmosphere. Jupiter and Saturn both show an increase in metals (Atreya et al. 2003; Flasar et al. 2005), and an enhancement of metals in the atmospheres of hot-jupiter is a well known consequence predicted by the core accretion model. An enhancement in the abundance in potassium high in the

154 The Atmospheres of Exoplanets RP /RS Wavelength [Å] Figure 4.5: The HST/STIS G430L transmission spectrum from Nikolov et al. (2014) and the 1σ uncertainties (shaded region) showing the best fit Rayleigh slope (dashed line) giving a temperature of K assuming a pure H 2 solar composition gas. atmosphere can however not explain the large absorption measured as a 10 increase in abundance compared to the base would be required. This is an unlikely explanation for the height increase, as the ionisation of potassium is expected to increase with altitude, resulting in a decrease in abundance of neutral potassium at high altitudes. The condensation of potassium at the base of the atmosphere, where the temperatures are cooler, could cause a depletion of potassium, thus serving to increase the relative abundance higher up (a cold trap). The most likely condensate to form would be KCl which would happen at a temperature of 600 K and at a pressure of 10 3 bar (Morley et al. 2012) which is too far away from the conditions of the base of the atmosphere to be a viable explanation. The photon dissociation by UV flux could break molecular hydrogen into atomic hydrogen at pressures lower than 10 8 bar (García Muñoz 2007) and could increase scale height, leading to an increase in the observed radius ratio. This would have the effect of lowering the mean molecular weight at the top of the atmosphere, by no more than a factor 2, and therefore photon dissociation can only partly account for the large absorption observed.

155 The Atmospheres of Exoplanets Resolution (λ/ λ) Na I Resolution (λ/ λ) K I Rp/R Å 75 Å 12 Å 75 Å Bin Width [Å] Bin Width [Å] Figure 4.6: Changes in the planet-to-star radius ratio as function of bin width and resolution for a 1332 K isothermal model (solid blue lines) measured by centring a bin on the D2 sodium (left) and a D2 potassium line core (right). The response is modeled with a box function. The black horizontal lines in the right hand plot show the difference in radius ratio introduced when binning the data from a 75 to a 12 Å bin, R pl /R = The vertical axis are in units of radius ratios above the white light curve radius ratio. The slight increase in radius ratio seen at 12 Å in the left plot and 68 Å in the plot on the right is due to the 5.98 Å and 34 Å separation between the D1 and D2 doublets of the sodium and potassium lines being included in the bin The effects of resolution The HST observations of Nikolov et al. (2014) showed no detection of potassium with a 75 Å bin centred on the feature resulting in a radius ratio of R pl /R = ± Compared to the GTC observations centred on the D2 potassium line at Å which resulted in R pl /R = ± a radius ratio difference of R pl /R = ± is observed. As the GTC observations of the central potassium line are done at a resolution of R = λ/ λ = 639 ( λ 12 Å) compared to the HST observation with a resolution of R=102 ( λ 75 Å) we explored the effects of resolution on the measurements. We measure the changes in the planet-to-star radius ratio as function of bin width and resolution for the HST observations by stepwise binning a high resolution sodium and potassium profile model centred on the D2 sodium and D2 potassium line. For the HST line spread function we used a box function. The increase in radius ratio as a function of decreasing bin width and increasing resolution is shown in Fig The increase in the planet-to-star radius ratio resulting from a decrease

156 The Atmospheres of Exoplanets 130 in bin width from 75 to 12 Å for the HST data, is measured to be R pl /R = for the potassium line. Compared to the observed difference in radius ratio of R pl /R = ± between the HST and GTC observations, it is clear that the difference in resolution alone can not explain why the large potassium absorption seen in the GTC data is not seen in the HST data. Attempts at binning the HST data down to 12 Å size bins (corresponding to a width of 2 pixels on the detector) resulted in a non detectable increase in the radius ratio. However, at such small bin sizes the uncertainties on the HST data become too large for a statistical significant non-detection to be not possible The effects of stellar variability Stellar variability is know to alter the flux received from the host star, thereby directly affecting the measured transit depth. HAT-P-1 b is not considered to be an active star, showing low chromospheric activity (Bakos et al. 2007; Knutson et al. 2010) without detectable spot crossings in the HST light curves and variability monitoring showing a < 0.05 per cent variability (Nikolov et al. 2014) corresponding to R pl /R Stellar variability is therefore unlikely to be the main cause behind the observed difference The effects of systematics Observations done on the 19 November 2010 and 26 November 2013, which used the same instrument setup, both show a clear increase in the radius ratio at the potassium probing wavelengths and Å compared to both the HST observations and the GTC observation at Å (green hexagon in Fig. 4.3). With such a large difference in radius ratio we investigated the scenario whereby the measurements at the potassium probing wavelengths are offset due to an unknown systematic caused by differences introduced by Earth s atmosphere. To address this concern we calculate the weighted mean of the difference in radius ratios between the potassium probing wavelengths at and Å obtained on the same night. By comparing the difference in radius ratios derived from the two light curves (using the same systematics models) obtained near simultaneously on the same night, the effects of the systematics as well as the choice of systematics models are greatly reduced. A combined difference of R pl /R = ±

157 The Atmospheres of Exoplanets 131 is measured, resulting in an independent detection of potassium with a 3.2 σ significance. 4.2 Conclusions We present three GTC/OSIRIS transit observations aimed at probing the presence of potassium in the atmosphere of HAT-P-1b. Two separate transit observations detect the potassium feature at high confidence providing a detection with a 6.7 σ significance at Å and 10.1 σ significance at Å when combined, relative to previous HST measurements. The strong potassium signature is modeled using a potassium profile which allows us to derive a temperature of T = 1332 ± 407 K at the pressures where the potassium is probed. A best-fit Rayleigh slope to previously obtained HST data results in a temperature of T = K (assuming molecular hydrogen dominates). The derived temperatures together with an enhanced potassium feature support a modest temperature inversion. The strong presence of potassium inferred from the observations could be influenced by the dissociation of molecular hydrogen into atomic hydrogen thereby decreasing the mean molecular weight or due to a super solar abundance of potassium, although it is likely that an increase in temperature at altitude is the dominant cause for the detection of potassium. Finally we discuss how spectral resolution affects radius ratio measurements. Although the effect is clearly present, it is not large enough to account for the large difference in radius ratio in the core of the potassium line compared to previous studies. Future observations aimed at sampling the slope of the potassium profile, will provide more stringent constraints on the derived temperature at the potassium probing wavelengths, and will allow for the degeneracies amongst the possible effects causing the large absorption to minimised.

158

159 The Atmospheres of Exoplanets A Search for Methane in the Atmosphere of GJ 1214b via GTC Narrow-Band Transmission Spectrophotometry Abstract We present narrow-band photometric measurements of the exoplanet GJ 1214b using the 10.4 m Gran Telescopio Canarias (GTC) and the OSIRIS instrument. Using tuneable filters we observed a total of five transits, three of which were observed at two wavelengths nearly simultaneously, producing a total of eight individual light curves, six of these probed the possible existence of a methane absorption feature in the Å region at high resolution. We detect no increase in the planet-to-star radius ratio across the methane feature with a change in radius ratio of R = ± corresponding to a scale height (H) change of 0.5±1.2 H across the methane feature, assuming a hydrogen dominated atmosphere. We find a variety of water and cloudy atmospheric models fit the data well, but find that cloud-free models provide poor fits. These observations support a flat transmission spectrum resulting from the presence of a high-altitude haze or a water-rich atmosphere, in agreement with previous studies. In this study the observations are predominantly limited by the photometric quality and the limited number of data points (resulting from a long observing cadence), which make the determination of the systematic noise challenging. With tuneable filters capable of high resolution measurements (R ) of narrow absorption features, the interpretation of our results are also limited by the absence of high resolution methane models below 1 µm Introduction The discovery of close-in super-earths, with masses between 1.5 and 10 M, has opened an entirely new field of exoplanet research. While transiting super Earths allow the radius and mass to be measured, the regime is prone to large degeneracies between their internal and atmospheric compositions and their masses (Rogers & Seager 2010). Characterising the atmospheres may be the only way to help constrain the overall bulk composition of these hot planets. A large planet-to-star

160 The Atmospheres of Exoplanets 134 contrast is essential when measuring transmission or emission spectra, making transiting super Earths orbiting M dwarf stars ideal for such studies. The most studied super Earth is GJ 1214b, discovered in the MEarth groundbased transit survey (Charbonneau et al. 2009). GJ 1214b is a 2.7 R, 6.55 M planet orbiting (P=1.58 days) a M4.5 dwarf star, and therefore has a large planetto-star radius ratio despite the stellar radius only being 0.21 R. The result is a transit depth of nearly 1.5%. The observed mass and radius of GJ 1214b are consistent with theoretical models indicative of a significant atmosphere (Miller- Ricci & Fortney 2010). Due to degeneracies in the models it is predicted that GJ 1214b is either composed of a rocky/ice core surrounded by a hydrogen-rich atmosphere, a water/ice core with an atmosphere dominated by water vapor, or a rocky core with a thin atmosphere formed by outgassing (Rogers & Seager 2010). Recent studies have attempted to constrain GJ 1214b s atmosphere through transmission spectroscopy (Bean et al. 2011, 2010; Berta et al. 2012; Carter et al. 2011; Charbonneau et al. 2009; Colón & Gaidos 2013; Croll et al. 2011; Crossfield et al. 2011; de Mooij et al. 2012; Désert et al. 2011; Fraine et al. 2013; Kundurthy et al. 2011; Murgas et al. 2012; Narita et al. 2013, 2012; Sada et al. 2010; Teske et al. 2013). In a majority of these studies, it has been found that GJ 1214b has a flat, featureless spectrum, with no evidence of any significant features either at optical ( nm) or near-infrared ( µm) wavelengths. It is believed that the lack of significant features supports the presence of either a heavy, metal-rich atmosphere or optically thick clouds/hazes that produce a constant level of absorption across a large range of wavelengths. One exception is a study conducted by Croll et al. (2011). Specifically, they reported a significantly deeper transit depth at 2.15 µm, a wavelength where methane would be a viable source of opacity. To help reconcile these studies, we present narrow-band photometry of five transits of GJ 1214b, three of them around a methane absorption feature commonly found at optical wavelengths in the atmospheres of the jovian planets and Titan (Karkoschka 1994). The observations were acquired using the tuneable filter imaging mode on the Optical System for Imaging and low Resolution Integrated Spectroscopy (OSIRIS) instrument installed on the 10.4 m Gran Telescopio Canarias (GTC). Tuneable filters (TFs) have several advantages over low resolution spectroscopy; they provide accurate differential photometry whilst also allowing for relatively high resolution measurements (R ), compared to lowresolution grisms. The relatively high resolution has the advantage of tuning the

161 The Atmospheres of Exoplanets 135 filters to avoid prominent telluric lines (see Hanuschik 2003 for a high-resolution sky emission atlas). Since no diffraction gratings are used, TFs can be much more efficient (Colón et al. 2010; Sing et al. 2011), especially for observing atomic absorption features that typically have a narrow spectral range. Combining this technique with the 10.4 m aperture of the GTC telescope makes it possible to study the atmospheres of planets orbiting fainter stars compared to the hot Jupiters HD b and HD b, which have bright host stars and large atmospheric scale heights, making them two best studied cases thus far. The methane feature that we focus on is the blue edge of the methane absorption band at 8900 Å and is predicted to cause additional absorption during transit at a level of 0.1%, assuming a hydrogen-rich atmosphere (Berta et al. 2011). In 4.3.3, we describe our observations. In and 4.3.5, we describe our data reduction and analysis procedures. We present our results in 4.3.6, where we also discuss the implications of stellar activity, equilibrium cloud models and the possible presence of methane in the atmosphere of GJ 1214b. Finally, we conclude with a summary of our findings in Observations Photometric observations of GJ 1214b were conducted using the GTC telescope on La Palma. For all observations, we used the tuneable filter (TF) imaging mode on OSIRIS (Cepa 1998; Cepa et al. 2000, 2003) to acquire photometry within a bandpass of 12 Å. The TF imager allows for custom bandpasses with a central wavelength between nm and a FWHM of Å to be specified. Out of the five transits observed, three transits were observed in the Å region by alternating between two narrow bandpasses, each with a full width at half maximum (FWHM) of 12 Å, allowing us to perform near simultaneous photometry at two wavelengths. Observing one transit at two wavelengths simultaneously allows for a more accurate comparison between two wavelengths as systematic variations caused by varying weather conditions or stellar activity are likely to affect both light curves similarly. For the observations done at two wavelengths we specifically chose our bandpasses so that one was located in the continuum, at a shorter wavelength of 8770 Å and Å compared to the other band located at 8835 Å and Å, within the methane absorption band. As described in Colón et al. (2010) and Sing et al. (2011), another property of the TF imaging

162 The Atmospheres of Exoplanets 136 mode is that the effective wavelength decreases radially outward from the optical center, so we attempted to position the target and a single primary reference star (i.e., one most comparable in brightness to the target) at the same distance from the optical center so as to observe both stars at the same wavelengths. 4 The other reference stars were thus observed at slightly different wavelengths than the target, due to their different distances from the optical center. All observations were performed with 1 1 binning and a fast pixel readout rate of 500 khz, a gain of 1.46 e /ADU and a read noise of 8 e as well as a single window located on one CCD chip. The size of the window varied for each observation, but was chosen to be large enough so as to contain the target and several reference stars of similar brightness. Data points with analog-to-digital unit (ADU) counts larger than 45,000 were removed to ensure the measurements were taken in the linear regime of the CCD detector. The data presented in this paper originated from two separate observing programs by PI. D. Sing (ESO program 182.C-2018 see and ) and PI. K. Colón (GTC2-10AFLO and GTC4-11AFLO see , and ) and each had slightly different observing strategies. Further details regarding each specific transit observation are given in the following sections Å Transit, 17 August 2010 Observations of the 2010 August 17 transit were tuned to a target wavelength of 8100 Å, with the target 3.7 arc minutes away from the optical centre. observations began at 21:18 UT and ended at 23:29 UT, during which time the airmass ranged from 1.11 to Due to variable seeing, ranging from 0.7 to 1.2, the telescope was defocused to avoid saturation. Two reference stars were selected (more on the selection technique in 4.3.4). The observations were windowed using a pixel section on CCD1. Twelve images containing counts greater than ADU were removed to ensure linearity. The exposure time was kept at 60 s throughout the sequence, with a corresponding 12 s of readout time. 4 Due to technical issues, the positioning for some of the observations was not as expected, and the target and a single reference star were not always observed at the same exact wavelengths. See The

163 The Atmospheres of Exoplanets Å Transit, 2 June 2010 Observations of the 2010 June 2 transit were tuned to a target wavelength of 8550 Å, with the target 1.3 arc minutes from the optical centre. The observations began at 23:48 UT and ended at 03:04 UT, during which time the airmass ranged from 1.27 to Due to a technical problem with the secondary mirror, re-focusing was not possible during the whole sequence. This caused an increase in the full width at half-maximum (FWHM) of the Point Spread Function (PSF) of the stars from 0.9 to 1.9, resulting in a notable decrease in the peak counts levels. Three reference stars were selected. The observations were performed using CCD1 and no windowing was done. One data point with counts greater than ADU was removed to ensure linearity (see 4.3.4). The exposure time was kept at 120 s throughout the sequence, with a corresponding 24.5 s of readout time for the full frame and 8835 Å Transit, 28 August 2010 Observations of the 2010 August 28 transit were tuned to the target wavelengths of 8770 and 8835 Å, with the target 3.2 arc minutes from the optical centre. The observations were done by alternating between the two wavelengths in sets of two exposures at each wavelength. The seeing was variable throughout the observations, so the telescope was defocused and the exposure time was changed to avoid saturation. The observations were done in queue (service) mode. The exposure time started at 100 s and was later increased to 150 s and then to 200 s towards the end of the observations. The observations began at 22:00 UT and ended at 00:30 UT, during which time the airmass ranged from 1.26 to 2.32 and the FWHM varied between 1.0 to 2.6. There are some small gaps in the data towards the beginning of the observations due to minor technical issues. Also, there is some vignetting in the last few images due to the low elevation of the telescope, so we exclude these from our analysis. Two reference stars were selected. Two data points with counts greater than ADU were removed to ensure linearity. The observations were windowed using a pixel section on CCD2 with a corresponding 22 s of readout time.

164 The Atmospheres of Exoplanets 138 Figure 4.7: A surface plot of GJ 1214 showing an uneven PSF due to a misalignment of the M1 mirror during the 8770 and 8835 Å observations on the 10 th of June 2011 (see Section ). The small bump seen towards the front of the larger PSF is due to one of the hexagonal mirrors not being properly aligned. By choosing a larger photometry aperture, the effects caused by the distorted PSF were removed and 8835 Å Transit, 10 June 2011 Observations of the 2011 June 11 transit were tuned to the target wavelengths of 8770 and 8835 Å, with the target 3.2 arc minutes from the optical centre. The observations were done by alternating between the two wavelengths in sets of two exposures at each wavelength. The conditions were clear, and observations took place during bright time in visitor mode. Observations began at 23:40 UT and ended at 02:48 UT, during which time the airmass ranged from 1.09 to 1.19 and the FWHM varied between 1.3 and 2.2. The observations started 25 min later than planned because one of the M1 mirror segments was found to be slightly misaligned (see Fig. 4.7). One segment of the mirror would not stack with the other segments. Attempts were made to correct this, although the problem persisted throughout the observations. As this problem had the same effect on all the stars (i.e., each star had an extended PSF, see Fig. 4.7), we have assumed the photometry was not significantly affected by this problem since we chose a larger aperture that included the photons from the unstacked segment. Three reference stars were selected. The observations were windowed using a pixel section on CCD1. An exposure time of 100 s was used throughout the sequence, with a corresponding 19 s of readout time.

165 The Atmospheres of Exoplanets ADUs Exposure time [s] Figure 4.8: The OSIRIS CCD1 (red) and CCD2 (blue) 500kHz exposure curves showing the linearity of the detector. The measurements connected by a solid line were used to fit the estimated linearity of the detector. Images which had the brighter reference star at more than 45,000 ADUs were removed in order to ensure they used data sampled within the linear regime of the CCD and Å Transit, 21 July 2010 Observations of the 2010 July 22 transit were tuned to the target wavelengths of and Å, with the target 2.9 arc minutes from the optical centre. The observations were done by alternating between the two wavelengths in sets of two exposures at each wavelength. The conditions were clear and the observations took place during bright time in queue mode. The observations began at 00:26 UT and ended at 02:11 UT. The airmass ranged from 1.25 to The actual seeing varied between 0.9 and 1.4. A slight defocus was used in order to avoid saturation. Two reference stars were selected. The observations were windowed using a pixel section on CCD2. An exposure time of 120 s was used throughout the sequence, with a corresponding 22 s of readout time.

166 The Atmospheres of Exoplanets Data Reduction For all our data sets, we used standard IRAF 5 procedures for bias subtraction and flat-field correction. For the flat-field correction, we used dome flats that were taken after each observation and for each filter setting. For the observations done at the methane probing wavelengths 8770 Å (two transits), Å, Å (two transits) and Å were affected by the presence of sky lines. We therefore performed a sky subtraction of these images using the IRAF package TFred 6. Aperture photometry was done using the APPHOT package in IRAF. To obtain the best possible photometry, a large number of apertures and sky annuli were explored. The aperture and sky annulus combination which produced the least amount of scatter in the continuum (lowest χ 2 value by fitting a straight line to the continuum) was chosen. The number of reference stars varied depending on the size of the CCD readout window, the location of the sky lines as well as the observed scatter in the photometry of each reference star. To determine the optimal number of reference stars all stars above 15,000 ADU were initially chosen as potential reference stars. Each star which did not help reduce the overall scatter in the continuum, such as fainter stars affected by the sky emission rings (see ) were removed. The linearities of the CCD1 and CCD2 detectors were evaluated by measuring the average ADU counts of centrally windowed flat field images as a function of exposure time (see Fig. 4.8). Using the measured points known to be within the linear regime of the CCD (< 25,000 ADU), a linear extrapolation of ADUs as a function of exposure time was created. To ensure the observations were not affected by non-linearity effects, the few images that contained a reference star with more than 45,000 ADUs were discarded, as counts above this level were shown to deviate from the linear extrapolation by more than 1σ on CCD2. The resulting light curves are shown in Fig and IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science Foundation. 6 Written by D. H. Jones for the Taurus Tunable Filter, previously installed on the Anglo- Australian Telescope;

167 The Atmospheres of Exoplanets σ R P /R S σ 3σ Sky slope Figure 4.9: The posterior MCMC distribution showing the relationship between the radius ratio and the slope of the sky term for the Å observations on the 10 th of June The different shadings represents the 1σ (dark-blue), 2σ (mid-blue) and 3σ (light-blue) confidence intervals Analysis Light curve fits The transit light curves were fitted using the analytical transit equations of Mandel & Agol (2002). The best fit light curve, together with the uncertainties associated with the fits, were determined by performing a Markov chain Monte Carlo algorithm (MCMC); see, Gregory (2005) for the use of MCMC in uncertainty estimates, Collier Cameron et al. (2007) for the application to transit fitting, and Pont et al. (2009) for our specific implementation. This gave us a posterior probability distribution which we used to define the uncertainties (see and Fig. 4.9). For a discussion on how the short baselines affect the radius ratio uncertainties, we refer the reader to Appendix Individual light curve fits were generated for each transit corresponding to different wavelengths. The initial starting parameters were from Bean et al. (2011); see below. We used 5 chains each consisting of 500,000 steps, trimming away the first 50,000 points with a 25% of the proposed parameter steps being accepted.

168 The Atmospheres of Exoplanets Relative Flux A A Relative Flux A OH-line A Relative Flux A Phase A Phase Figure 4.10: Shown are the raw (non-detrended) transit light curves at the off-methane target wavelengths 8770 Å (two transits) and Å (on the left) and the methane probing target wavelengths Å (two transits) and Å (on the right). The hollow white points represent the best-fit model. The red vertical line shows the phase during which the 8835 Å 10 th of June 2011 transit shows a wavelength drift across a strong OH emission line doublet near Å (see ) Relative Flux A A Phase Phase Figure 4.11: The GTC OSIRIS narrow band light curves with the target wavelength tuned to Å (left) and Å (right). Below each light curve are the residuals from the best fit. The Å light curve has a considerable shallower transit depth compared to the other transits. This could be due, in part, to a below average number of star spots on the surface of GJ 1214 effectively creating a shallower transit depth.

169 The Atmospheres of Exoplanets 143 Relative Flux A A Relative Flux A A Relative Flux A A Phase Phase Figure 4.12: The GTC OSIRIS narrow band light curves at the off-methane target wavelengths 8770 Å (two transits) and Å (on the left) and the methane probing target wavelengths Å (two transits) and Å (on the right). Below each light curve are the residuals from the best fit. The free parameters in the fit were the radius ratio, R p /R s and the sky-ring positions outlined in and summarised in Table The fixed parameters were the period P = days, mid-transit time T 0 = BJD TDB (see Table 4.2 for calculated ephemerides), impact parameter b = and the quadratic limb-darkening coefficients, u 1 and u 2, which varied depending on the wavelength of the observations. The stellar and orbital parameters were also kept fixed with R s = 0.21 R, the eccentricity e = 0 and the scaled semimajor axis a/r s = We fix these values to allow for a more accurate comparison with Bean et al. (2010), Désert et al. (2011), Croll et al. (2011) and Berta et al. (2012). The limb darkening coefficients used were calculated using the ATLAS stellar

170 The Atmospheres of Exoplanets 144 Figure 4.13: These two images exemplify the drift in OH sky emission observed during an observing sequence. The image on the left was taken at the beginning of the sequence, whilst the image on the right was taken towards the end of the sequence during the Å observations on the 10 th of June For some of the observations a linear correlation with sky line position was found and used to detrend the systematic effects it was causing in the data.